He was suspicious of banks circulating their own paper. So if you put a dollar of hard currency in a bank, it will give you a paper note worth one dollar that can be used to redeem the currency. But the bank's business is to make loans, so they will write another note (not backed by anything) and make a loan. As long as few people withdraw their currency, no one will notice that there is more paper than currency, leaving banks with the control of the money supply.

Jefferson wanted Congress to control the money supply, as the Constitution gives them the power to do.