Bodhicitta is often translated as 'awakening mind' or 'mind of enlightenment' and sometimes as 'universal altruism'. It refers to the state of mind that wishes to attain enlightenment for the sake of all sentient beings. The classic work on generating bodhicitta is Shantideva's Guide to the bodhisattva's way of life (Batchelor 1979).
Bodhicitta can be experienced physically in the heart region as the strong feeling that the heart is beating out into the world. Anyone, Buddhist or not, can experience bodhicitta, as is evident from the following haunting passage by a man who was participating in a healing group for people with cancer and almost certainly unacquainted with Buddhist thought.
... While we were doing imagery, one man said he experienced a sensation in his chest that was unfamiliar to him. It was as if he had always lived from his gut, and suddenly his energy, or life, had moved up into his chest. It was a very powerful experience which ended with the spontaneous image of a hawk riding, balanced, on the updraft. I asked him how he felt about that, and he said the hawk was precarious and alive, and it could see a long, long way. And then he said, "You know, the experiencing of opening your heart is precarious and alive, and you can see a long, long way." And then there was a long pause, and he said, "It's the only thing worth doing."
Source: Bill Moyers. 1993. Healing and the mind. Doubleday. 349-350.