I've been working all week on an article on Buddha Nature. Buddha Nature is a Mahayana doctrine that defies explanation. English language syntax, the whole subject-verb-object thing, makes it very difficult to speak of Buddha Nature without getting it wrong.
For example, it's common to say that all beings have Buddha Nature. Beings (subject) have (verb) Buddha Nature (object). That's how English, and many other languages, work. It's just about impossible to say anything in English without falling into that pattern, somehow.
So there are beings, and Buddha Nature, but a being is not really a subject and Buddha Nature is not really an object, and "has" is just all wrong.
Mahayana says that Buddha Nature is the fundamental nature of all beings. Theravadins argue, with some justification, that Buddha Nature is just a means to sneak a self, an atman, back into Buddhism. I say "with some justification" because I have read essays about Buddha Nature that make it sound like the atman doctrine of the early Vedic religion, just with different labels.
The atman of the Vedic religions, and Hinduism today, was thought of as the essential nature of individuals that is also identical with Brahman, the absolute or source of reality. Some scholars of Hinduism describe the individual as a "pot" for the essence of Brahman. The Buddha explicitly denied this doctrine, teaching instead anatman, no self.
When you hear that all beings have Buddha Nature, it's really easy to conceptualize something just like atman, an essence that one possesses that is identical with some universal transcendent Buddha. But the Buddha rejected such a concept.
In Rinzai Zen, the koan Mu works to dissolve the "me and my Buddha Nature" dichotomy. Dogen, the great patriarch of Japanese Soto Zen, stressed that Buddha Nature is not something we have; it's closer to say it's what we are. See Dogen's Bussho, Buddha Nature, chapter 22 of the 95-Fascicle Shobogenzo, to see a real master take on the subject-verb-object barrier and smash it to bits.
This isn't easy. Anyone who thinks it is simple to understand doesn't understand it. The best most of us can do is to try hard to not get stuck in conceptualizations while staying open to realization. And practice, practice, practice.