Fiat money is any money declared by a government to be legal tender which is neither legally convertible to any other thing, nor fixed in value in terms of any objective standard.
The term derives from the Latin fiat, meaning "let it be done". Where fiat money is used as currency, the term fiat currency is used. Today, most national currencies are fiat currencies, including the US dollar, the euro, and all other reserve currencies.
To boil it down, fiat currencies such as the US dollar only have value because the government says it does. It is not backed by anything tangible what so ever. Nothing. No Gold, Silver, Land, Oil: nothing. Our gold standard history has long been replaced by fiat money. This allows the government to create as much fiat money as they want. The only limiting factor comes into play when people lose confidence and believe that their fiat dollars are worthless and stop accepting them.
The scary part of this fiat money is that to keep the value of a dollar up we depend on a number of foreign interests to continue accepting dollars in large amounts, such as the Chinese, Japanese and many oil producing nations. If any of these nations simply slow down the rate at which they are willing to accept our dollars the value of the dollar would drop significantly.