From AionSource.com Wiki
A quest in role playing games, including massively multiplayer online role-playing games (MMORPGs), is a task that a player controlled character or group of characters may complete in order to gain a reward. Rewards may include an increase in the character's experience in order to learn new skills and abilities, loot or treasure, in-game currency such as gold coins, access to new locations or areas, or any combination of the above.
Quests are typically grouped in to one of four categories: Kill quests, gather quests, delivery quests and escort quests. Quests can be linked together to form quest series or chains. In this manner, quests are used to provide the player with further background to the setting their characters are in. This mechanism is also used to advance any story or plot the game might have.
taken from Wikipedia