Quests are tasks that players are able to perform for NPCs in exchange for a reward. There are many quests available to players, each having certain requirements that a player must meet before being able to take on the quest. Some of these requirements include being a certain level, having a mininum amount of fame, holding a certain item, etc.
There are various types of quests that are available. These types include monster-killing quests and item-gathering quests. By completing a quest, players will earn a reward; rewards may include Mesos, items, and experience.
Players can view their quest log by pressing the (by default) Q key. In this window are three panes: one displays quests that they have not taken on yet; one displays quests that are currently outstanding and require completion; and one displays quests that they have completed.