From TheWarWiki

Quests are the basic method of leveling one's character. There are various types of quests:

• Kill Quests - kill mobs and collect items off them.
• Influence Quests - and you may be granted additional quests.
• Exploration Quests - Explore an area, or walk to an NPC and talk to that person.
• Realm vs Realm (RvR) Quests - Capture battlefield objectives or kill enemy players!
• Public Quests (PQ) - They have various stages and anybody in the area can participate in them.
• Timed Quests - Some quests are timed and require you to complete an objective within certain time limits.

Almost all of the above quests (excluding Public Quests) work in the following way: Collect the quest from the NPC quest giver, complete it, and return to either the NPC quest giver or the designated location / NPC. Some quests require you to complete them by clicking on the quest item in your backpack. Upon handing in the quest, you are granted a certain amount of experience points and may be rewarded with items of varying value.