In Buddhism buddha nature has many names, and depend on what Buddha was talking about, he liked to give it different names. Names such as Buddha nature, Boddhi mind, ultimate mind, pure mind, pure awareness, ultimate reality, bare knowingness, emptiness, no mind are some of the words that point directly at the Awaken. In the beginning of Buddha's teaching he never talked about this mind. For him it is important that people learned to let go. Anything that our thinking mind can grasp at, is a defect on the path of enlightenment. Therefore Buddha wanted people to let go. "To let go" does not mean to reject, but to have a relax relation to whatever it is.
Buddha was actually a very clever man and a good teacher. His knowledge was divided into three periods of teaching. The first period is called "The first turning of the wheel". During this first period he stated that life contained suffering. There is a way out of suffering, and the path to end suffering. Actually during this time he never really talked about what Buddha nature is. The goal of this teaching was to reach Nirvana, the end of suffering.
In the "Second turning of the wheel" he talked about the inherit aspect of every phenomena. During this period he talked much about Emptiness, emptiness of self, of no-self, of suffering, of duality...ect. In short everything is egoless. Nothing can exist by its own. It needs everything else in order to come into existence. Even if it seems to come into existence, it is never really there. It is only a vast emptiness display as a magical illusion before our eyes/senses. From this teaching the sutra Prajnaparamita came into the world. During this time whoever encountered Buddha was influenced by his talk about egolessness and his knowledge of Emptiness. In this period he stated, there is no enlightenment nor end of enlightenment. There is no Nirvana, no Samsara, no ignorance nor end of ignorance. Everything was just a vast Emptiness!
People who did not understood him thought, there was nothing at all. They thought everything was just a great blank and void nothingness, but this was not the case. Buddha didn't mean that there was absolutely nothing. Many people - still today - have misunderstood this aspect of Buddha's teaching. To believe there is absolutely nothing then who is it that seemingly live in this physical body?
So because Buddha was concerned that a number of people misunderstood his teaching and hold on that nothing - absolutely nothing - exist then he did the "Third turning of the wheel". During this period he pointed directly at the mind and said within Emptiness something seems to be there. It is not a thing, a subject, a object but a mere Knowingness, Pure Awareness; Buddha mind. It does not belong to anyone, it is not a self, not a body, not a thought. It is pure beyond the concept of being born and not born. It is the Knower without anyone who knows. It is the Witness without anyone witnessing. It is beyond words or any conceptual construct. It has always been there, but if we try to find it (as an object to identify) we have missed the point, have not understood the teaching. It has the capacity to know itself, know about its presence, but it can never look at it, because it is not an object, a subject or any sensory phenomena.
This marked the last teaching of the Buddha. Just before he died, he said "Take my dharma as your light. Walk the path and exam my words!".