The bank is the part of the shop where you can trade credits for cash. The ability to buy credits is unavailable during the beta phase, but they should be purchasable here sometime in the future.
This is where managers buy items to place in their gyms. These items then gradually generate prestige, and most of these items are used in training fighters.
This is where managers hire gym trainers and fight coaches, who, in combination with appropriate equipment, are required for the training of fighters.
This is where managers can purchase new gyms.