Well, there are actually a number of different characteristics that are shared by the vast majority of MMOs that make them completely different than other games out there on the market. For example, MMOs offer a stable, alter-universe that will exist and continue playing no matter if gamers are online or not – the sun sets, the sun rises, and it doesn't matter who is there to see it. While the majority of MMO games emphasize multiplayer options and play, these games will continue to run with artificial intelligence on the client that the game is set on, which allows players to log in and play, but also does not allow players to “beat” the game as they would in a normal PC or console game.
But, MMO's also share several other characteristics between them that set them apart from other games. For example, they host a large group of players in one game area, or world, and all of these players can play together – either on the same side or against them – at any time they log into the game. So, what constitutes an MMO and just a game that offers multiplayer action? Well, typically, MMO games have over 50 players online at any time, per server or client, according to Wikipedia. Those games that have under 50 players online at any time and play on private servers, such as Half-Life.
There are many people out there in the game industry who are still debating whether a high player count on each server is the qualifying mark that will classify a game as an MMO or not, while others argue that it is the size of the in-game world itself and the ability of that world to support a large number of players, no matter if it does or not. The reason behind the last argument is that most games that fall right on the line of the MMO definition, usually have the ability to support a large number of gamers, such as in the thousands, on one server at any time.
Now, to help support all of the masses of players on an MMO, the game will need several servers that can support the online gamers and worlds, unlike a normal pc or console game that only needs the game itself to support one player. Most MMO games feature multiple servers, where the world is always the same, but different players play on different servers and the players on one server don't come into contact with players on another server. These are called “sharded” universes, and many of the more popular MMO games on the market will have over 10 of these servers, sometimes up towards a hundred servers running at one time.