If you believe in reincarnation, you believe that after death a person's soul is reborn in another body. Certain religions hold this belief as a central tenet, including Hinduism and Buddhism.
The noun reincarnation comes from the Latin roots re, meaning again, and incarnare, meaning to make flesh. The word reincarnation does not have to be a literal rebirth, however. The term can be used to mean a more figurative reinvention or rebirth. Your dad may have spent twenty years of his life working as a stockbroker, but after he reinvented himself, you'd be proud of his reincarnation as a math teacher.