The personal bank has twelve slots for a character's storage and eight shared slots which may be accessed by all characters on an account, with some exceptions:
You can increase your storage space by adding bags and boxes to your bank slots. LORE items can go in your shared bank slots, but cannot be picked up by characters that already have that item. HEIRLOOM items are normally untradable specifically allowed to be traded between characters on the same account via the shared bank slots.
LORE items can go in the guild bank, but cannot be picked up by characters that already have that item.
The guild bank starts with four tabs with 10 slots each. Available bank space will grow as your guild levels up; you'll gain an additional row of 10 slots in each tab at guild levels 10, 20, 30, 40, 50, 60 and 80. Guild leaders can grant and restrict access to the guild bank tabs through the guild window.
There are many bank customizations available at EQ2 Interface.