A fiat money is a type of currency that is declared legal tender by a government but has no intrinsic or fixed value and is not backed by any tangible asset, such as gold or silver. Fiat currency values are guaranteed by the government that issues the money, and the government can control the supply of money in circulation in response to economic fluctuations.
The American Monetary Association provides this explanation of what fiat means in relation to monetary systems:
The word “fiat” is Latin in origin and refers to an arbitrary order issued by a government or other authoritative figure. When applied to paper money, fiat currency refers to the scary notion that our dollar has value only because the government says it does.
The United States Dollar (USD), the Euro and most other major currencies are fiat monies. The main alternative to fiat currencies is commodity money, which is backed by a tangible asset. The USD, for example, was previously backed by a specific amount of gold, and people could convert one into the other.
President Richard Nixon ended the gold standard in the United States in 1971, when he fixed the rate at $38 dollars per ounce of gold and said that dollars could no longer be redeemed with gold. The values of gold and the USD were decoupled entirely in 1976.