In Hindu and Buddhist theology as it pertains to reincarnation, an anagami (or anaagaamii) is a "non-returner"; after death, he will not be reborn back into the human world, and will instead appear in one of the Brahma worlds called the Pure Abodes. He will attain Nirvana there.
An Anagami has abandoned the five lower fetters that bind the mind to the cycle of rebirth. An Anagami is thus partially enlightened, and on the way to perfect and complete Enlightenment.