Fiat currency is a currency which is not backed by any physical commodity, such as gold or silver. The value of the currency is derived from the relationship between supply and demand and stability of the government. The U.S. dollar is now valued based on supply and demand and faith in the U.S. government.
Fiat currency is a flexible currency and provides the opportunity to control over the economy by the issuing government. But on other hand fiat currency losing value by inflation or at the event of hyperinflation the currency becomes worthless. The value of the fiat currency is solemnly depends on the faith of the population, in case of people lose faith the currency will drop the value.