Quests can be done instead of expeditions. To do so you need to activate those in the settings.
The tavern is the place where you can select and accept a quest. The quest givers are next to the counter.
You always get three quests to choose from which offer you different gold rewards, XP (experience points) and occasionally an item, but only if you successfully complete the quest, of course. Each quest consumes a certain amount of Thirst for Adventure. You can see how much thirst is left by looking at the displayed meter in the tavern.
After starting a quest, the Thirst for Adventure runs automatically. A timer informs you how long you are still on the quest.
If you move the mouse pointer over the quest name, the quest task can be read again.