Missions are a great way to earn gems and other rewards (such as avatars), just for completing certain in-game tasks such as collecting food and iron or expanding your base.
You can find your Missions on the bottom of your screen, just open the scroll and quill icon to track your progress.
There are different stages of Missions which are identified by the Roman numerals (I, II, III, IV, V and so on). Each stage has its own goal and progress.
Note, these are different than your Wanted Missions.