The Bank is where your items are stored. Weapons and armour can be equipped in a menu opened by clicking on the item in the bank. Bank slots can be bought in the shop. You can sell your items with the menu opened by clicking on the item in your inventory.
When you start the game, you only have 4 bank slots available. The player can buy more bank slots in the Shop. The cost for bank slots gets increasingly more expensive until they cap out at 4 million gp each at a little over 100 slots.