MMORPG stands for:
Massive-Multiplayer-Online-Role-Playing-Game
In these games players take the role of characters and interact with many other players, and non-player characters, in an ever-evolving world. Unlike many other games, when the player leave an MMORPG game the time in the game continues to pass by, the storyline continues to evolve, and other players continue to play.
The player goals in MMORPG games vary greatly but almost always foster collaboration with other players. Characters in these games are usually highly customizable and are able to progress and advance their stats through playing and/or collecting or purchasing in-game items.
The most popular example of a MMORPG game is World of Warcraft.