Transmigration is the movement of a soul into another body after death. Transmigration is related to reincarnation. If you believe your cat is your reincarnated grandmother, then you believe in transmigration.
The pieces of this word might look familiar — trans means “across,” as in transport or transcontinental, and migration is the act of moving, like birds flying south. Transmigration used to just mean what it sounds like, as in “move from one place to another,” but later it took on the deeper meaning of a soul moving into another body after death. Various religions are associated with different types of transmigration.