In Sanskrit, bodhi means "awakened" and chitta means "mind" or "heart." Bodhichitta -- "awakened heart-mind" -- is the compassionate wish to realize enlightenment for all beings, not just oneself. Through bodhichitta, the desire to attain enlightenment transcends the narrow interests of the individual self.
Bodhichitta is an essential part of Mahayana Buddhism. Without bodhichitta, the path to enlightenment is mired in selfishness. However hard we work we are still wrapped up in our own heads, our own pain, our own wants. The path to awakening opens when it becomes unselfish and compassionate.
Tibetan Buddhism further divides bodhichitta into relative and absolute aspects. Relative bodhichitta is the wish to be enlightened for the sake of all beings. Absolute bodhichitta is direct insight into the absolute nature of being.