Tavern displays quests that can be completed for different rewards. The tavern unlocks at Level 28.
The quests will reset daily or can be refreshed any time with (10 Gems for every unlocked quest).
1-Star and 2-Star quests can be completed immediately for free. Other quests can be completed immediately by spending Gems.
Locking a quest will "save" it from being auto refreshed the next day. By locking a quest you also lock 1 of your refreshes, so if your maximum is 5 quests, but 1 is locked, you will get 4 new quests the next day and will have your same, locked one.
Another way to 'save' quests is to complete the quest, but not redeem it, this will lock your heroes to the quest, but will grant you a new quest the next day. So, if your maximum is 5 quests, but 1 is completed (and not redeemed), the next day you will get 5 new quests next to your unredeemed one.