A bank is a type of building that shows up in cities. While the bank itself stores nothing and has no obvious physical mechanism to function, the bank's empty vault is one of the sites a warlord or courtier assigned as city manager must "inspect". A city with a bank receives a small boost to the Shmuckers it produces for the side each turn, and a larger boost if the city is actively managed.
A bank can also act like a small, temporary treasury. If a side's capital falls, a very small pool of Shmuckers may remain in the bank. The amount in the bank is unknown even to the ruler, but the figure can be divined by a Moneymancer or Mathamancer. Bank money cannot be accessed or spent in any way, but in the absence of a treasury (or a zero balance in the side's treasury) it will automagically pay the upkeep of some or all units which start their next turn in that city. This will continue until the bank has no money left. Banks slowly fill up each turn the side's treasury is active, and can become completely full. The maximum capacity of a bank can be divined (by a Mathamancer, Moneymancer, or Dirtamancer), and increased (by a Moneymancer or Dirtamancer). A small gain in the city's Shmucker production may indicate that a bank has filled up, and the excess is appearing in the side's treasury. Having money in the bank will not prevent a city from going barbarian if the side falls completely.
Banks can be created at will when a ruler orders a city to upgrade to a level 2 or higher, as one of the limited number of desired features he or she can fix in mind. Banks can also be added to any city by a Dirtamancer or Moneymancer.