Fiat is covered in full under Fiat Currency, which explains how government-issued money works, its history and its strengths and weaknesses. This page gives a short definition and explains how the shortened word is used in crypto.
Fiat money is currency that has value because a government declares it legal tender and people accept it, rather than because it can be exchanged for a fixed amount of gold or another commodity. The US dollar, the euro and the Japanese yen are all fiat currencies. Their supply is managed by central banks, which use interest rates and other tools to try to keep inflation under control. The word comes from Latin fiat, "let it be done", reflecting the idea that the money exists by decree. Most countries abandoned direct links to gold during the twentieth century, a shift described under the gold standard.
In crypto, "fiat" is used as a short noun for ordinary money, as opposed to cryptocurrency. A fiat on-ramp lets users buy crypto with bank money, and a fiat-backed stablecoin is a token meant to hold the value of a national currency. The shorthand is informal; economists and central banks normally say fiat money or fiat currency in full.