Taverns in towns offer more than just rumors; they also provide 'Propositions' – optional quests that your generic units can undertake. These propositions are time-based and require specific job levels or stats from your units. Sending units on propositions can earn you gil, experience, and sometimes unique items.
While your units are on a proposition, they are unavailable for battles. It's a good way to level up units you're not actively using or to earn passive income. Pay attention to the success rate of each proposition, as failing can result in lost time and no reward. Some propositions even unlock new locations or events.