Ascension is the act of delivering the Amulet of Yendor to your god and winning the game.
The end of game message given upon ascension is:
You offer the Amulet of Yendor to [your god]... An invisible choir sings, and you are bathed in radiance... The voice of [your god] booms out: "Congratulations, mortal!" "In return to thy service, I grant thee the gift of Immortality!" You ascend to the status of Demigod[dess]...
Ascending is difficult. There are players who claim to have played for decades without ascending, although their number has been reduced in recent years as the Internet has provided easy access to spoilers.