Banks are used to store items in Albion Online. There is a bank in every major city, there are also guild banks and personal banks which can be accessed through a guild island or player island respectively.
Banks can also be found in different maps in black/blue/yellow/red zones in War Camps that are marked on the map with an orange-black flag. Also, a major part of the territories that are controlled by a guild has a bank where you can stash items.
Items that were stashed in a bank can't be accessed through other banks.
Example: If you stored an Adept's Guardian Armor in Fort Sterling's bank you can't take it from Thetford Bank.