Metempsychosis is the belief that the soul can migrate from the body after death to inhabit another body: reincarnation, in other words. As Sonya goes on to say, the Ancient Egyptians believed in the transmigration of the soul after death. Evidence for this can be found in their many Books of the Dead. They later came to believe that souls could be reborn in new generations as a way of explaining family likenesses.
The idea of reincarnation also occurred in Ancient Greek thought, possibly as a result of contact with Egypt. Today, the most widespread belief in reincarnation occurs in Hinduism, where it is believed that the soul will be reincarnated as a higher or more lowly species depending upon its behaviour during its current life.