Clarifying point: MMO's are not just fantasy games! MMO's consist of Hello Kitty to starships and everything in between.
What is an MMO?
MMO is an acronym for Mass Multiplayer Online Game, MMO's as they are known today have been around since 1996. Todays MMO's tend to have many different aspects that make it an MMO; Some aspects are an Auction House, Chat System, Currency, Level System, Reputation, Profesions, Class Abilities, Multiple Races, Quests/Missions, Loot. Many more aspects are involved in an MMO, they are most commonly know for their subscription fees and the no-lifers who play them. MMO's are usually RPG's, short for Roleplaying Games, where each person has their own customizable character/avatar, and live the story of the game through the characters eyes.
Formal Definition of MMO.
A massively multiplayer online game. A computer game in which a large number of players can simultaneously interact in a persistent world. http://en.wiktionary.org/wiki/MMO
The differences between MMO's and other videogames.
MMO
Players share the same world.
Quests and missions.
Some MMO's costs money to play.
Customizable interface.
Loot tables.
Raids.
Patches/updates.
Videogames
Can choose to play single player of multiplayer, if multiplayer is offerred.
No subscription fees. Excluding (Xbox Live/ PSN).
Not updated, game is as is. Except for Multiplayer Map Packs, usually found in games like Call of Duty and Halo.
Levels -> Different than how it is referred to in MMO's Levels in Non-MMO videogames are different stage of story mode, think of mario, the next stage. Some RPG's use MMO way of levels.