A fiat currency is a currency issued and controlled by a central government. Fiat currencies are often not backed by physical commodities (i.e. precious metals, diamonds, etc.). Rather, the value of fiat money is largely determined by the government that issues it, which can manipulate the currency through changing its circulating supply (among other methods). Fiat currencies derive value from their status as legal tender, and their largely value depends on the stability of the issuing government and the strength of its economy.
For example, the U.S. dollar, which was initially backed by gold, became fully a fiat currency in 1971 when President Nixon fully abandoned the "gold standard." However, the size and relatively low inflation of the United States economy has allowed the dollar to retain significant value. Fiat currencies issued by unstable governments with weak economies are generally at greater risk of devaluation. For example, the value of the Zimbabwe dollar plummeted in 2008, as the country’s economy experienced inflation of up to 500B percent.