Bankers and moneylenders allow you to store items so that you don't have to carry them around all the time. You may also use them to transfer items between characters on the same account. For a fee, you can increase the number of items you may store there. Note that there is only one actual bank storage in the game - if you deposit an item in one bank, you can withdraw it from any other bank.
Bankers also offer access to your guild banks and stores. Moneylenders do not have this facility.
Moneylenders can be found in outlaws refuges.