Every day, Travian Kingdoms lets you complete mini-quests to earn some rewards.
To view these daily quests, open the quest book by clicking on the appropriate icon on the left of your village view: then open the "Daily Quest" tab.
There are three quest slots in your book. Each can contain a task to complete. It means you can store a maximum of 3 daily quests at a time. Click on the quest name to see the task to be done.
Once you've completed a quest, you can collect the reward, and the slot will be emptied. A new quest will appear in this slot after some time (a countdown shows you the exact moment)
If you're not interested in a specific quest or you don't think you can complete it, you can exchange it for a new task by clicking on the icon at the bottom of the screen: