In Brogue, the term ascension is synonomus with a "successful ascent", "winning" or "beating the game". It occurs when a player retrieves the Amulet of Yendor and escapes the Dungeons of Doom by returning to the dungeon entrance on level 1. When people talk about beating Brogue, this is typically what they are referring to.
In Brogue, players have the option to continue deeper after finding the Amulet, in an attempt to find lumenstones to increase their score upon ascent. Some even attempt to proceed all the way to level 40 in search of a mastery.