The Bank is the place to go when you want to store your hard earned gold or withdraw it for a spending spree.
Depositing your gold into the bank will save you from losing any of it to the 1% gold-in-hand tax at major Resets, or having it stolen by Orcs who have a racial ability to steal gold. Info on this can be found at Races.
Also, if you have a listing to buy items at the Greedy Market in Silver Meadows you must have gold in your bank to complete transactions.
If you have debt from defaulting on a loan or get negative gold by any other means, 70% of all money that touches you hand is taken off and put towards your debt (which will be a separate place displayed under your bank) So for example if you sell something on the markets when you withdraw the money from your bank, 70% of it will be deducted.