What, exactly, is fiat currency?

what is the deal with fiat currency? how does it arise and where does it attain its exchange-value? i'm currently participating in the hexbear capital reading group and in chapters 2 and 3 marx goes heavily into the way that gold standard money becomes exchange-value. fiat money is discussed only a little, and somewhat dismissively, although as far as i can tell none of the actual theory of the time precludes it from existing. are there any texts that go into it in detail?

important context: https://lemmygrad.ml/post/10346359/7603669