Regulated, government-issued currency that is not backed by anything of inherent value. Like the kind you use to buy a sandwich at the deli.
US dollars, Mexican pesos and Chinese yuans are all forms of Fiat.
A service that allows you to convert fiat currency in to cryptocurrency.
Cryptocurrency exchanges that deal in fiat currency, cryptocurrency brokerages and cryptocurrency ATMs are all examples of fiat gateways.
Coinbase is a fiat gateway because it allows you to purchase Bitcoin/Ethereum/Litecoin with fiat currency such as US dollars.