The game plays out even when the player is not logged in or running the game. The player character does not necessarily do anything during this time, but can be interacted by the environment and other players where available.
Alternate name: Offline progress
The first video game about Background progress was released in 1989.
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.