No, it’s not money made from old, crushed Italian automobiles.
Fiat money is money that has value only because of government regulation or law. The term derives from the Latin fiat, meaning “let it be done”, as such money is established by government decree. Where fiat money is used as currency, the term fiat currency is used.
Fiat money originated in 11th century China, and its use became widespread during the Yuan and Ming dynasties. The Nixon Shock of 1971 ended the direct convertibility of the United States dollar to gold. Since then all reserve currencies have been fiat currencies, including the dollar and the euro.
In short, fiat money includes almost all the money we use in the U.S., including coins and paper money. It has value because the government backs it, not because that piece of paper is actually worth one dollar, or a hundred dollars.
This contrasts with money made from precious metals, like gold. Gold coins are valuable because the gold in the coin equals the amount of money on its face — in the old days. Precious metals carry a lot more value today than they did 50 years ago. A silver dollar used to be worth one dollar; today that same amount of silver is worth $30 or $40.
What kind of fiat money do you know about?