Fiat currency is used by every country in the world. Fiat is the currency tied to the nation state that is not backed by any physical commodity. Prior to fiat currency, countries would back their money supply with an equivalent value in a commodity such as gold.
Fiat has a value because the Government of the country through their actions and policies maintain the value as a status quo. People also must agree that the currency has value. Fiat in a country is controlled by a central bank.
The central bank can print more fiat and this is where inflation rears its ugly head. As alluded to earlier in this guide, cryptocurrency can solve the inflation issue by having a capped total supply.