Money taking the form of a commodity with intrinsic value is known as commodity money. An item has intrinsic value if it has value outside of its use as money. Cigarettes are used as a medium of exchange by American prisoners, but they also have value outside of their use as money. Specifically, cigarettes can be smoked.
Money whose value derives from government decree is known as fiat money. U.S. dollars have value because the U.S. government stands behind them. Each U.S. note reads, "This note is legal tender for all debts, public and private." Through its central bank, the U.S. government declares that U.S. dollars are valid, and it does a reasonably good job of managing their circulation. Ultimately, however, the dollar has value because people are willing to accept it in exchange for goods and services with confidence that they can then use it to buy other goods and services.