Owning a fief allows you to collect taxes from the populace every week (taxes accumulate, so you don't have to visit every week) Note: in Warband you do not have to visit at all to collect taxes,you automatically receive them. Towns earn the most base taxes, villages second, and castles the least. The prosperity of each fief also affects the amount of taxes they produce. You can raise the prosperity of a town by making sure that its caravans reach their destinations, and by completing quests from its Guildmaster. For villages, stop it from being raided, kill bandits if they invade, build improvements, and get quests from its Village Elder. Also, when repeatedly purchasing imported goods from a town or village, the prosperity will eventually drop due to the lack of these goods, and they will no longer be available untill trade has returned them, which can take a rather long time.
Tax efficiency reflects the amount of trade being lost to bandits and enemies