Fiat currency is money that a government issues and that is not backed by a commodity such as gold or silver. Most global currencies are "fiat currencies," including the US dollar, the euro, and the great british**.
Sling Money stores your balance in digital currencies called USDP and EURC, but you can display your balance and transactions in whatever fiat currency you like. This means your displayed balance may sometimes change as currency exchange rates fluctuate.
** For UK-based residents, Sling Money is only available in a Closed Beta.