A Bank is an area where players can deposit their surplus goods. There are banks in each of the four major cities of Mirith, Marali, Lerilin, and Andris. If there are others, they are not widely known. Deposits made in any Oberin bank can be withdrawn from any other Oberin bank (including rare items). A player's bank account has the same number of inventory slots as a chest or character inventory.
Bank accounts are capped at 10,000,000gp. Deposits in excess of this amount are destroyed. Stackable items deposited (such as potions, bandages, skulls, dragon scales, etc) are capped at 50,000 of that item.
The amount of a gold that a character may simultaneously deposit and/or withdraw is effectively capped at 999,999 gp. Any amount deposited and/or withdrawn in excess of this limit will cause the offending character's file to be corrupted and essentially deleted, with no chance of recovery. It's not the amount of gold in one's Inventory that poses a risk of file corruption, but the amount moved.
Banks are also the standard gathering place in each Oberin city. At any given time, over half the players in each city with be standing at its bank. Most clerics and druids perform their alchemy while standing at the bank (to be able to deposit their products directly into their bank accounts; same for etherite-"heavy" wizards). Plate classes (if not low-capped in the skill, otherwise less-) commonly gather at the bank to practice the Anatomy skill.
Players who spend more of their time at Banks than in the wild are commonly referred to as "Bank Tarts".