Buddha Nature is a term used often inMahayana 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.