Fiat means force.

Fiat does not mean money without intrinsic value, though it is typical that if it is fiat, intrinsic value can be dispensed with.
For example, the US Dollar was fiat even when there was silver in the coins (up to the early 60's).

Fiat money is money that has the force of law.  The Legal Tender law means that the fiat currency discharges a debt when offered.
This means that you can eat at a restaurant, and the restaurant is free to accept any sort of payment that you agree to, but if you are in the US and offer them dollars they can not then say "no we only accept payment in live rabbits" and hold you for non-payment in rabbits.  You have a debt for the food you ate, and legal tender will discharge that debt.