Banking facilitates the transfer of wealth in an economy. In its most simple form, rather than having someone carry around all their money, they keep it in a bank. When they need that money, they write a check or use a debit card. This ensures a safe transfer of money from one person to another.
In the United States, we have a dual banking system, meaning that we have banks that are chartered nationally in addition to banks that function under a state charter and regulations.