“All beings are Buddhas,
But obscured by incidental stains.
When those have been removed, there is Buddhahood.” — Third Karmapa Rangjun Dorje 
Buddha Nature (Buddha Dhatu) is one of the most important and inspirational foundation understandings in Mahayana Buddhism — possibly the most important. The symbol of the Lotus — while it means many things — is the most striking symbol of Buddha Nature: the Lotus flower (our Buddha Nature) emerging from the muck in the bottom of the pond (our defilements and attachments) — yet untouched by the mud.
The quickest definition of Buddha Nature would be: the Luminous mind of all sentient beings that eventually, cleared of all defilements, will become Buddha. In other words, all beings have the potential to be Buddha.
“Buddha nature is all-encompassing … This Buddha nature is present just as the shining sun is present in the sky.” — Tulku Urgyen Rinpoche
The sun may be hidden by clouds, but it is always there. Our Buddha Nature, likewise, maybe obscured by our attachments and defilements, but it is always there. It’s not something we have (like a soul) but something we are.
In teachings by Khenop Tsultrim Tenzin, the teacher explained it this way: “Impurities and defilements are the fruition of mistaken view… When defilements are removed (it is like) when the sun is freed from the clouds, then all the sun quality is there.” 
Dzogchen Ponlop Rinpoche defined Buddha Nature as: “… our fundamental nature of mind is a luminous expanse of awareness that is beyond all conceptual fabrication and completely free from the movement of thoughts. It is the union of emptiness and clarity, of space and radiant awareness that is endowed with supreme and immeasurable qualities.” 
Why Buddha Nature is not soul
From a western perspective, it is important to remove any immediate comparisons to soul. Buddha Nature is not soul as understood in non-Buddhist traditions. Because Buddha taught “impermanence” and the importance of removing our attachment to ego, Buddha Nature is not similar to the soul. (Not referring to Hindu Atman, but rather Judeo Christian soul.)
“In Buddhism we don’t have a soul, we don’t have a concept of soul.” said Venerable Zasep Rinpoche [in a soon to be released video on Buddha Nature.] “To me, soul sounds like some sort of permanent thing, within us. Nothing is permanent. Instead of soul, we have consciousness, mind stream, and Buddha Nature.” 
The two ways that both Buddha Nature and soul are actually similar is in the concept of being both “natural” and “luminous.” Where they absolutely differ is on the concept of ego and self; soul implies permanent attachment to a “self” which, at its core, is the opposite of the Buddhist ideal of Emptiness.
Also, in most traditions, happiness of the soul rely on the blessings of God. In Buddhism, you could say it is completely self-help — only you can develop your Buddha Nature. (People, Yidams, Buddhas can help, but ultimately you have to do it.)
If it is not the soul, what is Buddha Nature?
Buddha Nature is a lofty concept, understood by Enlightened Beings, but in a certain way unteachable to the unenlightened. In the Uttaratantra it says:
“It is subtle, so it is not the object of learning.
It is ultimate, so it is not the object of contemplation.
The dharmata is profound, so it is not the object of mundane meditation…”
Realizing it is there, as taught by infallible Buddhas, is uplifting and wonderful. Understanding exactly what it is more difficult. It can be discussed, to a certain extent taught or commented upon, but ultimately it is “ultimate” wisdom, far beyond our current ability to fully grasp. On that level, it requires faith. But, for those who accept the infallible teachings of Buddha, it is not faith, but acceptance of truth we don’t yet fully understand. Even though we can’t fully understand, it is important to know we have Buddha Nature.
Two Types of Buddha Nature: Natural and Developing
Zasep Rinpoche explains that there are actually two types of Buddha Nature (Tathagatagharba):
“Natural Tathagatagarbha is something that is with us always, and developing Tathagatagarbha means that we have to develop. So, in other words, the consciousness, our consciousness, is developing Tathagatagarbha.
” Our consciousness is perceiving and imputing labels on objects, seeing things as subject and object, and relationship between subject and object. The subject and object of consciousness is inter-dependent. Dependent arising. There is no inherent existence. Therefore, the true nature of the consciousness is Shunyata. The ultimate nature of the mind is Empty, like it states in the Heart Sutra: “Likewise, consciousness is Empty, and Emptiness is also consciousness.” Consciousness is emptiness. So, natural Tathagatagarbha is the emptiness of the mind.”
The Dalai Lama: “Even insects have Buddha Nature”
The Dalai Lama, in a teaching on Buddha Nature said: ” From Buddha’s viewpoint, a human being has—through training, through practice—has what we call the highest enlightened mental state. So through practice, a human being, through a sort of purification one’s own mental state, can eventually, finally, become an enlightened one. Even Buddha himself, in order to get final enlightenment, needed hard work…
” Every sentient being—even insects—have Buddha nature. The seed of Buddha means consciousness, the cognitive power—the seed of enlightenment. That’s from Buddha’s viewpoint. All these destructive things can be removed from the mind, so therefore there’s no reason to believe some sentient beings cannot become Buddha. So every sentient being has that seed.” 
At the same time, the Dalai Lama cautioned that Buddha Nature, while a liberating concept, and an optimistic one, is influenced and developed only by you, yourself. No one can do it for you.
“Buddha also stated you are your own master. Future, everything depends on your own shoulder. Buddha’s responsibility is just to show the path, that’s all.”
Buddhist Sutras teaching Buddha Nature
The sources of teachings on Buddha Nature are extensive:
- Tathāgatagarbha Sūtra
- Śrīmālādevī Siṃhanāda Sūtra
- Anunatva Apurnatva Nirdeśa
- Aṅgulimālīya Sūtra
- Ratnagotravibhāga, a compendium of Tathāgatagarbha-thought
- Mahāyāna Mahāparinirvāṇa Sūtra
- Laṅkāvatāra Sūtra
Luminous Mind similar to Buddha Nature
Although Buddha Nature is a vital teaching in Mahayana Buddhism, it is not — in those terms — expressed in Therevadan traditions, where instead they refer to the Pali Tipitika and Shakyamuni Buddha’s teaching on Luminous mind. Luminous Mind is similar in concept the Buddha Nature in some ways, and many equate the two — since Buddha, in Pali Canon, described that luminous mind is present whether you are aware of it or not — that it is mind “freed from incoming defilements.” A mind free of defilements is clearly the first step on the path to an Enlightened Mind.
The Pali Tipitika (Pabhassara Sutta, Anguttara Nikaya 1.49-52:
“Luminous, monks, is the mind. And it is defiled by incoming defilements. The uninstructed run-of-the-mill person doesn’t discern that as it actually is present, which is why I tell you that — for the uninstructed run-of-the-mill person — there is no development of the mind.
“Luminous, monks, is the mind. And it is freed from incoming defilements. The well-instructed disciple of the noble ones discerns that as it actually is present, which is why I tell you that — for the well-instructed disciple of the noble ones — there is development of the mind.”
Luminous mind is a core teaching of all Buddhist schools. Often the analogy of the “sun” is taught, with Luminous Buddha Mind being the sun, but our defilements, negative karmas and strong attachments to our ego are like dark clouds obscuring the sun.
The Root Text
The Treatise entitled: “A Teaching on the Essence of the Tathagatas
by the Third Karmapa, Rangjung Dorje
Translated by Peter Roberts
at Sonada Monastery near Darjeeling in June 1990,
from a five-folio xylograph printed at Rumtek Monastery, Sikkim
Verse divisions and translation are based on
Jamgon Kongrtrul Lodro Thaye’s commentary to this text,
a forty-one-folio xylograph made at Rumtek Monastery, Sikkim, entitled
“An Illumination to ‘The Treatise that Teaches the Buddha Nature’ –
I pay homage to all the Buddhas and Bodhisattvas.
“Though beginningless, it has an end.
It is pure by nature and has the quality of permanence.
It is unseen because it is obscured by a beginningless covering.
Like, for example, a golden statue that has been obscured.”
That was taught (by the Buddha).
“The element of the beginningless time
Is the location of all phenomena.
Due to its existence, there are all beings
And also the attainment of nirvana.”
(That was taught by the Buddha.)
“All beings are Buddhas,
But obscured by incidental stains.
When those have been removed, there is Buddhahood.”
That is a quotation from a Tantra.
The “element” has no creator,
But is given this name because it retains its own characteristics.
“Beginningless” means that
There is nothing previous to it.
The “time” is that very instant.
It hasn’t come from somewhere else.
“Phenomena” are explained to be
Samsara and nirvana appearing as a duality.
This is named “the ground of the latencies of ignorance.”
The movement of mental events, correct thoughts
And incorrect thoughts are the cause of that arising (of samsara and nirvana).
The condition for their causes is taught to be the alaya (the universal ground).
The “location” is the Buddha nature.
Incorrect conceptualisation is completely located within the mind’s purity.
This purity that exists in that way
Exists, but is not seen due to ignorant conceptualisation.
Therefore, there is samsara.
If they are dispelled, there is nirvana,
Which is termed “the end.”
“Beginning” and “end” are dependent upon conceptualisation.
Mental events are like winds
That cause karma and kleshas to arise.
The (karma and kleshas) manifest the skandhas, dhatus,
Ayatanas, and all the phenomena of dualistic appearances.
Someone who strives for and discards these (appearances) is deluded.
What can be negated through rejecting your own projections?
What can be gained by acquiring your own projections?
Isn’t this belief in duality a fraud?
Though this understanding is taught as a remedy,
The understanding of non-duality is not truth.
It is not conception of non-conceptuality.
The understanding of emptiness gained through breaking down forms and so on,
Isn’t it itself a delusion?
But it is taught so that attachment to things as real will cease.
There isn’t anything that is either real or false.
The wise have said that everything is like the moon’s reflection on water.
The “ordinary mind” is called
The “dharmadhatu” and “the Buddha nature.”
The enlightened cannot improve it.
Unenlightened beings cannot corrupt it.
It is described by many names,
But its meaning cannot be known through verbal expression.
It is unceasing manifestation.
(It is taught) to have sixty-four qualities.
Though this is (just) a simplified description,
It is said that each of the sixty-four has millions (of qualities).
There are ten strengths:
(1) the knowledge of appropriate and inappropriate actions;
(2) the knowledge of the ripening of karma,
(3) of natures,
(4) aptitudes, and
(6) the knowledge of the destinations of all paths,
(7) (the possession) of dhyana;
(8) divine sight,
(9) the memory of previous lives, and
Due to those (ten strengths), there are the four fearlessnesses:
(1) teaching that one abides in enlightenment, within all phenomena,
(2) teaching the path,
(3) teaching cessation, and
(4) being beyond dispute.
Due to those causes there are these eighteen (distinct qualities):
(1) no error,
(2) no empty chatter,
(3) no forgetfulness,
(4) continuous meditation,
(5) the absence of a variety of identifications,
(6) the absence of an undiscriminating neutrality,
(7) the possession of an undeteriorating aspiration,
(12) the wisdom that sees complete liberation,
(13)-(15) every action being preceded by wisdom, and
(16)-(18) time being unable to obscure.
If those thirty-two (qualities) are possessed, there is the dharmakaya.
In our present (state), we deny the (presence of the Buddha nature) and these qualities.
There is no understanding of it as it is.
The non-existent “fabrications” are conceived of as existent.
The “completely true” is not known.
Thus we create our own torment.
Oh! Understanding these qualities of the dharmakaya
To be true is the knowledge of truth,
But in their present state, beings with meagre ability
Reject the knowledge of truth and fabricate untruth,
Which is adopted by the agitation that follows it.
Through knowing (the Buddha nature) as it is
One obtains its powers.
There is nothing whatever to be removed;
There isn’t the slightest thing that needs to be added.
The truth is truly seen.
If the truth is seen, there is complete liberation.
The “element” is devoid of the incidental impurities,
Which have the characteristic of being separate.
It is not devoid of the unsurpassable qualities,
Which have the characteristic of inseparability.
In (the Buddha nature) are the qualities of the two form kayas:
The thirty-two major and (eighty) secondary signs.
Those qualities that are attained are one’s own body.
The body is not created by self, Phwya, Shiva, Brahma, external real particles,
Or by elements beyond experience.
When the impure development of the five senses,
When the (duality) of perceiver and perceived
Is purified, the name “attainment” is given.
Therefore, the purified nadis, vayus, and bindus are the pure form kayas.
The unpurified are the impure form kayas.
For example, the qualities of an encrusted
Beryl are not evident.
When it is cleaned with yak-hair cloth and salty-water,
And cleaned with vinegar and woollen cloth,
Purified, it becomes the jewel that fulfils all needs and desires.
In the same way, for the purpose of clearing away
The three encrustations of the kleshas, knowledge, and meditation
From the aquamarine of the mind,
There is their total cessation through the paths of accumulation and juncture,
The seven impure bhumis and their pure bhumis.
When incorrect conceptualisation
Encounters correct conceptualisation,
Just as both (kindling-) sticks are burned by the fire, there is freedom from (both) conceptualisations.
There is freedom from the concepts of elimination,
Remedies, suchness, and the idea of a result.
At that time, the flowers of the physical signs blossom
In the one who has the body of space.
The three phases of impurity, both purity and impurity,
And of complete purity are respectively:
(The phases) of beings, Bodhisattvas, and the Tathagatas.
Though this is what is said, Buddhahood is not newly created.
As it was before, it is the same after.
It is the changeless Buddha nature.
The “change” is becoming free of the stains.
If someone has the negative view
That the Buddha qualities have no cause,
Or conceive them not to be within oneself,
But created by external causes and conditions,
What difference is there between that and the eternalist and nihilist views of non-Buddhists?
The apparent momentary birth and cessation of the “mental events” (of Buddhas)
Correspond to the impure mental events (of beings).
If (the mental events of the Buddhas) were not like that,
The activity of the form kayas would cease.
However, they are not given the name “mental events,”
But (the name) “discriminating wisdom.”
The nature of material elements
Is (either) accompanied by clinging (or) their powerful essence is manifested.
There is no difference whatsoever in appearances
To the deluded and the undeluded.
The (only) difference is the presence or absence of clinging to dualism.
If that was not so,
How could the Buddhas apply their activity?
The examples of the wish-fulfilling jewel and so on
Are explained to represent the manifestation of non-conceptual power.
However, this does not exist solely within the beings of others.
If that were so, it would be the wisdom of other beings.
And if that were so, then wisdom would be delusion.
If one states that (wisdom) has attachment for its own appearances,
Then a mirror that has appearances within it
Would (also) have thoughts of attachment.
All the delusions that beings have
Appear to (a Buddha’s) wisdom.
The wisdom is however unstained by the delusions.
For example, though the material elements
Appear to originate and cease within space,
Space is unstained, is without any origin or cessation.
In that same way, though the wisdom of the Buddhas
Enters beings, it is not stained.
It is not given the name “delusion.”
It is called “(the wisdom of) accomplishment of action.”
The mind that has the absence of the three obscurations
Is “(the wisdom of) equality” and it is “peace.”
Due to having love and great compassion (for beings)
The sambhoga(kaya), etc., appears to them.
This is stated in order to refute those who say
That the attainment of Buddhahood is the same as the Hinayana (attainment).
Wisdom is the three permanences:
Permanence of nature is the dharmakaya;
Permanence of continuity is the sambhogakaya;
Uninterruptedness is the nirmanakaya.
There are three impermanences:
Mentally fabricated emptiness is impermanent;
The mind of moving thoughts is impermanent;
The composite six consciousnesses are impermanent.
However, the three permanences are present.
The three impermanences are stains.
The three permanences are wisdom.
This is not the same as the Tirthika “self,”
Because that is a mental fabrication and (Buddha nature) is not.
This is not the same as the nirvana of the Shravakas and Pratyekabuddhas
Because (in that) all the qualities of the form kayas are not manifested.
This is not the same as the body of an (ordinary) being
Because it is not created due to the defilements.
It will not change back to the previous state
Because it has manifested exactly as it is.
There will never (again) be the appearance of the stains
Because there is freedom from differentiating conceptualisation.
Therefore, the mind, this Buddha,
Is present now, but is not known.
(From the “Sutralankara”):
“When there is realization, at that time,
Just as when the heat of metal ceases,
And conjunctivitis in the eyes cease,
Because Buddhahood (has occurred), one cannot say that
Mind and wisdom either exist or do not exist.”
(From the “Mahayanavimshika”):
“Because in the pristine meaning there is no birth,
There is also no liberation there.
Buddhahood is like space.
It has the same qualities as beings.
As ‘this side’ and ‘the opposite side’ are birthless,
The composites are truly empty.
This is the experience of omniscient wisdom.”
(From the “Uttaratantra”)
“It is subtle, so it is not the object of learning.
It is ultimate, so it is not the object of contemplation.
The dharmata is profound, so it is not the object of
Mundane meditation, and so on.”
This experience of wisdom that knows itself,
This ultimate arises through trust in self-origination.
Oh! Because they do not understand this,
The children wander in the ocean of samsara!
Through the power of great Shakyamuni,
Of Manjushri, Maitreya, and Avalokiteshvara,
This was written by Rangjung Dorje.
May all beings have unmistaken knowledge
And full attainment of the Buddha nature!
This completes the definitive presentation of the Buddha nature,
which is the essence of the vajrayana.
 Buddha Weekly Video releasing in July: ” What is the difference between Tathagatagarbha Buddha Nature and the concept of soul?” taught by Venerable Zasep Tulku Rinpoche
 The Dalai Lama: “On Buddha Nature” http://www.pbs.org/thebuddha/blog/2010/Mar/9/dalai-lama-buddha-nature/
 Uttaratantra Shastra teachings by Khenpo Tsultrim Tenzin, November 15, 2015, Drikung TMC
 Venerable Khenchen Thrangu Rinpoche “The Buddha Nature”
Instructions on a Treatise entitled: “A Teaching on the Essence of the Tathagatas (The Tathagatagarbha)” by the Third Karmapa, Rangjung Dorje, according to “An Illumination of the Thoughts of Rangjung (Dorje): A Commentary to “The Treatise that Teaches the Buddha Nature” by Jamgon Kongtrul Lodro Thaye the Great Translated from Tibetan by Peter Roberts
 “Buddha Nature” https://www.thoughtco.com/buddha-nature-doctrine-450001