Quests on Armor Games are goals in different games you can do. In order to complete quests you have to have an ArmorGames account. Quests are completely optional and the only reward is bragging about how many quests you have completed. The way to view what you need to do to complete a quest is to hover over the picture of the quest and it will tell you what you have to do. Once you complete the quest it will show up on your ArmorGames profile.
Example of a QuestEdit
This is a picture of what a quest looks like.