The money supply of the US is what is called "fiat money." This is money that is simply backed by the faith that people have in the government of the United States.
The US money supply is not backed by anything like gold. The money itself has no inherent value whatsoever. The only reason that the US money has any value is because people think that it has value. People feel this way because they have faith in the government of the US. They believe that it will honor its debts and that its money will continue to have value.
Thus, the money supply of the US is backed only by the faith people have in the US government.