"When banks make loans, they create money. This is because money is really just an IOU. The role of the central bank is to preside over a legal order that effectively grants banks the exclusive right to create IOUs of a certain kind, ones that the government will recognise as legal tender by its willingness to accept them in payment of taxes. There's really no limit on how much banks could create, provided they can find someone willing to borrow it. They will never get caught short, for the simple reason that borrowers do not, generally speaking, take the cash and put it under their mattresses; ultimately, any money a bank loans out will just end up back in some bank again. So for the banking system as a whole, every loan just becomes another deposit."
—But wait, there's more.