MMORPG stands for Massive(ly) Mutliplayer Online Role Play(ing) Game and an MMORPG is simply a genre of computer game in which there are hundreds (usually thousands or even millions) of players from all across the world.
In most MMORPGs the player takes the role of his or her own character and must navigate some sort of world or realm in order to complete quests and tasks. Usually these worlds will be persistent, hosted on a permanent server, and actions taken by the players will have an affect on the realm or world. Thus making it interactive, even when the player is not playing the game. This is known as being "real time" and is how MMORPGs emulate the real world. In one particular instance in World of Warcraft, an event occurred where a spell effect which lowered the players health slowly over time was spread from player to player. The disease effect got out of hand and as players ran back to towns and cities the virus spread and became an epidemic. Later, a patch was released to remedy the problem, but the community was shocked at how closely the behaviour seen in the game resembled real life.
Most MMORPGs, such as World of Warcraft and Guildwars, are based in fantasy and myth and involve magic and spells. Some are based in space, where you must command a spacecraft or your own planet. Some are even based on the real world, and with the invention of Google maps it may well be possible to have an MMORPG world which closely emulates the real world, perhaps even being able to visit your own home!
MUDs, or Multi-User Dungeons, were the first MMORPGs. They are usually simple text based programs where the players use commands to control and interact with their character, the world, and other players. Although simple 2D graphical versions and even 3D MUDs do exist. Similar to MUDs are browser based MMORPGs, like RuneScape, which are played entirely in the users browser. They can be simple pages of text or complex 3D renderings and offer similar functionality of more developed MMORPGs, usually for free.
MMORPGs were virtually unknown a few years ago and now they are commonplace for most gamers. In fact worldwide revenues for MMORPGs exceeded half a billion dollars in 2005, and Western revenues exceeded one billion USD in 2006.