The only reason fiat money has value is because people accept that it has value. Sure fiat money used to be backed by gold or silver. But Gold and silver has value for the same reason. People hold money becuse it can be exchanged with goods or services. Some people have decided that they want to hold cryptocurrency instead as money. It's that simple.
If Bitcoin were to be accepted by all businesses and stores then I think many more people would start using it instead of fiat.