One who acts without desire effectively becomes Brahman, the universal Self, which is eternal. This is a state of realization that the individual’s ātman is the same as Brahman, the universe itself.
In this way, one escapes birth and death. This is a similar concept as nirvana (extinguishing the self or ego) in Buddhism, but in Hinduism Brahman is represented as a soul (ātman) within the individual, whereas in Buddhism the individual is ultimately empty, not substantial.