Background progress

For MMOs this means that the player character remains in the game world regardless if the player is logged in or not and performs basic duties there as dictated by AI. This may also mean the player's characters and such may be attacked during the time they aren't actively playing.

For offline games this likely means that the game either runs as a service/daemon or similar and continues progressing the game even when the main game application isn't running, or it progresses events proportional to the time since the game was last played as part of game launch.

This is the norm for many browser based strategy games.