'Reincarnation/Rebirth: Embodiment in a subsequent life.
The same person is not reborn but the mind follows its unenlightened habit to think that things are real. It consolidates itself in a new life according to the karma which has been built up through actions, words and thoughts and this mind experiences a new world accordingly.
Normally a reincarnation happens involuntarily but can also happen consciously on the basis of good wishes for the benefit of beings, if the nature of mind has been recognized and to a great extent.'
-- Quoted from 'The Way Things Are' by Lama Ole Nydahl.
See also, if You wish: Better Reincarnation, Phowa.