MMORPG is short for Massively Multiplayer Online Role-Playing Game; a type of computer game where players assume the role of a character in a virtual world populated by virtual characters. It is a variant of the RPG (Role Playing Game), a game (not necessarily a video or computer game) where players assume the role of a character in an imagined setting. World of Warcraft by Blizzard and Dark Age of Camelot by EA Mythic are two MMORPGs, as well as Warhammer Online: Age of Reckoning. The term "MMO" has also been used to describe other Online Games that are not necessarily RPGs.
See Wikipedia's article Massively multiplayer online role-playing game for more info.