A feature common for single player in computer games (especially first-person shooters). Quick save is, as the name states, a quick way to save the game. This is usually achieved by hitting whatever key has been designated for the action during the game, thus alleviating the necessity for the player to escape to a menu, select which file to save the game as (if the game gives that option, which some don't), and so on.
It might sound like a feature designed purely out of sloth but is a nice touch if a game's menu takes a while to load up or if the player is really into the feel of the game and doesn't want to interrupt that heightened video game alertness. Quick save's loading counterpart is aptly known as quick load.