The U.S. money supply is backed by faith in the value of money. There is an agreement among both parties in a transaction that money has a specific value. As long as the two parties agree on what that value is, then the money supply needs no actual material support.
Any currency backed simply by faith in the value of that currency by all parties involved with the currency is known as fiat currency. For short periods, the U.S. money supply was backed by gold and silver, where the federal government needed to have enough of the commodity on hand to cover the actual value of the money issued. The money could then be exchanged for the commodity itself at federal banks and repositories.
Even when the currency was backed by valuable commodities, it was still considered fiat money. The only difference being that instead of faith in the value of the currency, people had faith in the value of the commodity used as an anchor. Because there is no inherent value attached to U.S. currency, its value often changes based on the laws of supply and demand. The greater the demand for U.S. currency, the more it is worth, whereas, the more currency available on the market, the lower its worth.