Roleplay is assuming the persona (or role) of a character while in the game and acting out the character's spoken dialogue, actions, emotes, etc. It is like pretending to be someone you are not or someone you can never be. A key element of roleplaying is consistency, both of actions taken in the game and between in-game actions and pre-specified background information. Background information includes both decisions made during character creation (perhaps most notably alignment) and any background stories that may have been written for that character (including the background story of the gameworld). In particular, roleplayers should maintain a distinction between what the player knows and what the character knows, avoiding metagaming as much as possible.
Some players see roleplaying as diametrically opposed to powergaming (or "rollplaying", as in rolling dice). While powergaming does often involve metagaming for decision-making, it is not necessarily at odds with playing a role as sometimes a role can be invented that happens to fit the powergamer's goals. On the other hand, such invented roles are often (particularly when the player is inexperienced) "thin", "weak", or otherwise unacceptable to the more demanding roleplayers. Thus, there is a split between the two play styles, albeit not an unbridgeable gap.
There are many servers where roleplaying is either encouraged or even enforced. If not found in the "Role Play" category on GameSpy, such servers usually have a note about roleplaying in their description or website. Such servers often provide a forum where players can post their characters' background stories for others to read. (It may be important to note that these stories are posted for other players to read and are often not part of what other characters know.) On such servers, it is probably poor form to include these stories in a character's description (written during character creation); a physical description of the character is more appropriate in this case.