In a fiat money system, money is not backed by a physical commodity (i.e.: gold). Instead, the only thing that gives the money value is its relative scarcity and the faith placed in it by the people that use it.
In a fiat monetary system, there is no restrain on the amount of money that can be created. This allows unlimited credit creation. Initially, a rapid growth in the availability of credit is often mistaken for economic growth, as spending and business profits grow and frequently there is a rapid growth in equity prices. In the long run, however, the economy tends to suffer much more by the following contraction than it gained from the expansion in credit.
In most cases, a fiat monetary system comes into existence as a result of excessive public debt. When the government is unable to repay all its debt in gold or silver, the temptation to remove physical backing rather than to default becomes irresistible. This was the case in 18th century France during the Law scheme, as well as in the 70s in the US, when Nixon removed the last link between the dollar and gold which is still in effect today.