Buddha Nature is a term used often in Mahayana Buddhism that isn't easy to define. To add to the confusion, understanding of what it is varies from school to school.
Very basically, Buddha Nature is the fundamental nature of all beings. Because this is so, all beings may realize enlightenment. Beyond that, one can find all manner of commentaries and theories and doctrines about Buddha Nature that may be difficult to understand. This is because Buddha Nature is not part of our conventional, conceptual understanding of things, and language doesn't function well to explain it.
This article is intended to be a beginner's introduction to Buddha Nature for the completely confused.
Origin of the Buddha Nature Doctrine
The origin of the Buddha Nature doctrine can be traced to something the historical Buddha said, recorded in 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." [Thanissaro Bhikkhu translation]
This passage gave rise to many theories and interpretations within early Buddhism. Monastics and scholars also struggled with questions about anatta, no self, and how a no-self could be reborn, affected by karma, or become a Buddha. The luminous mind that is present whether one is aware of it or not offered an answer.
Theravada Buddhism did not develop a doctrine of Buddha Nature. However, other early schools of Buddhism began to describe the luminous mind is a subtle, basic consciousness present in all sentient beings, or as a potentiality for enlightenment that pervades everywhere.
Buddha Nature in China and Tibet
In the 5th century, a text called the Mahayana Mahaparinirvana Sutra -- or the Nirvana Sutra -- was translated from Sanskrit into Chinese. The Nirvana Sutra is one of three Mahayana sutras that make up a collection called the Tathagatagarbha ("womb of the Buddhas") sutras. Today some scholars believe these texts were developed from earlier Mahasanghika texts. Mahasanghika was an early sect of Buddhism that emerged in the 4th century BCE and which was an important forerunner of Mahayana.
The Tathagatagarbha sutras are credited with presenting the fully developed doctrine of Buddha Dhatu, or Buddha Nature. The Nirvana Sutra in particular was enormously influential in the development of Buddhism in China. Buddha Nature remains an essential teaching in the several schools of Mahayana Buddhism that emerged in China, such as T'ien T'ai and Chan (Zen).
At least some of the Tathagatagarbha sutras also were translated into Tibetan, probably late in the 8th century. Buddha Nature is an important teaching in Tibetan Buddhism, although the various schools of Tibetan Buddhism do not entirely agree on what it is. For example, the Sakya and Nyingma schools emphasize that Buddha Nature is the essential nature of the mind, while Gelugpa treats it more as a potentiality within the mind.
Note that "Tathagatagarbha" sometimes appears in texts as a synonym for Buddha Nature, although it doesn't mean exactly the same thing.
Is Buddha Nature a Self?
Sometimes Buddha Nature is described as a "true self" or "original self." And sometimes it is said that everyone has Buddha Nature. This is not wrong. But sometimes people hear this and imagine that Buddha Nature is something like a soul, or some attribute that we possess, like intelligence or a bad temper. This is not a correct view.
Smashing the "me and my Buddha nature" dichotomy appears to be the point of a famous dialogue between the Chan master Chao-chou Ts'ung-shen (778-897) and a monk, who inquired if a dog has Buddha nature. Chao-chou's answer -- Mu! (no, or does not have) has been contemplated as a koan by generations of Zen students.
Eihei Dogen (1200-1253) "made a paradigm shift when he translated a phrase rendered in the Chinese version of the Nirvana Sutra from 'All sentient beings have Buddha nature' to 'All existents are Buddha nature,'" wrote Buddhist scholar Paula Arai in Bringing Zen Home, the Healing Heart of Japanese Women's Rituals. "Moreover, by removing an explicit verb the whole phrase becomes an activity. The implications of this grammatical shift continue to reverberate. Some could interpret this move as the logical conclusion of a nondualistic philosophy."
Very simply, Dogen's point is that Buddha Nature is not something we have, it is what we are. And this something that we are is an activity or process that involves all beings. Dogen also emphasized that practice is not something that will give us enlightenment but instead is the activity of our already enlightened nature, or Buddha Nature.
Let's go back to the original idea of a luminous mind that is always present, whether we are aware of it or not. The Tibetan teacher Dzogchen Ponlop Rinpoche described Buddha Nature this way:
"... 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. From this basic nature of emptiness everything is expressed; from this everything arises and manifests."
Another way of putting this is to say that Buddha Nature is "something" -- perhaps not the right word, but I don't think there is a right word -- that you are, together with all beings. And this "something" is already enlightened. Because beings cling to a false idea of a finite self, set apart from everything else, they do not experience themselves as Buddhas. But when beings clarify the nature of their existence they experience the Buddha Nature that was always there.
If this explanation is not helping you at all, please don't be discouraged. It's better to not try to "figure it out." Keep open, and let it clarify itself.