Fiat money is “money that derives its value from government regulation or law. The term derives from the Latin fiat, meaning “let it be done” or “it shall be [money]”, as such money is established by government decree”.
The different types of money along history can be seen in this entry from the Wikipedia:
“Currently, most modern monetary systems are based on fiat money. However, for most of history, almost all money was commodity money, such as gold and silver coins. As economies developed, commodity money was eventually replaced by representative money, such as the gold standard, as traders found the physical transportation of gold and silver burdensome. Fiat currencies gradually took over in the last hundred years, especially since the breakup of the Bretton Woods system in the early 1970s.”
I found an interesting graphic in the book “This Time is Different” (C. Reinhart & K. Rogoff) where you can see how during several centuries governments debased or decreased the content of silver of its currency in order to get over heavy debts. The trend in the graphic seems to point at the “inevitability” of fiat money.
These debasements of course created inflation, which is nothing new, only the means have changed, as Carmen Reinhart and Kenneth Rogoff say in their book:
“[…] the shift from metallic to paper currency provides an important example of the fact that technological innovation does not necessarily create entirely new kinds of financial crises but can exacerbate their effects, much as technology has constantly made warfare more deadly over the course of history.”