"Persistent World" is a term often used to describe an online game world that continues to evolve and change over time. The players enter and exit the world at will, but the game world continues on with or without them. Occasionally, the players can affect the game world permanently through their actions, as well as game events occurring that alter the world in some way.
There are many massively multiplayer online games on the Internet that support the existence of several hundred or thousands of players to play at a time. These MassMOGs (or MMORPGs, MMOGs, etc..) are usually persistent-state worlds.