Tobin appears wrong that "Fiat money has no intrinsic non-monetary source of value." See
ELI5: What actually makes makes currency worth anything? : explainlikeimfive
One reason why fiat money has value, is that the government insists that people pay taxes, and the only payment of taxes they will accept is in their own currency. So, everyone has to earn or acquire enough in that currency to pay their taxes.
This r/explainlikeimfive comment by theelectricmayor answers your question. I edited punctuation and grammar.
Let's examine the idea that gold-backed money has value because gold has value. Does gold really have value?
Imagine you had a million dollars in gold coins, then all world governments and organizations vanished overnight. In this new Mad Max world, do you think you could walk over to your neighbor and buy some of his food with gold? After all what use is gold to him? He can't eat it, it won't protect him from the rain and it won't scare off wild dogs. It's just shiny metal that's too soft to be made into tools and frankly too heavy to lug around.
The reason a gold coin had value in the past was that, somewhere in every province was some powerful lord who had more food then he could ever eat, a big castle over his head and many guards with swords who knew how to deal with wild dogs. And with all of his needs well met, this lord could afford to trade some of his excess food or wood or swords for a pretty piece of metal to decorate his head with. So people used those gold coins in trade, because they knew that they could cash them out into something of true value (by trading with the lord of the castle), if they couldn't find someone that would accept them as a currency.
Of course, once more than a certain amount of gold coins circulates, gold coins in effect become a fiat currency, because the lord can only trade for so much gold before he run out of goods and there are only so many neighboring lords to try. So while this 'backing' of the gold currency existed it wasn't that robust. It would not survive a 'run on the bank' where everyone tried to cash out their gold coins at once.
Now let's imagine a different kingdom. This kingdom has fertile land and is protected from invaders because of the king's wise policies. Thus many farmers flock there to enjoy its bounty. However, in return for the use of the land, the king demands a yearly payment that can only be made using pieces of paper with the king's face stamped on them. The paper is worthless by itself, but because the chance to farm in this kingdom has value and you can't farm there without some of those papers, the papers gain value. People are willing to trade goods in exchange for these papers because then they can then can take a share of those fertile lands for a year. Indeed they now use the papers among themselves as a unit of value and even ask for it from outsiders — Those who wish to buy goods from those in the fertile kingdom now must obtain the paper its citizens value, which only makes the paper more valuable.
What I've just described is most fiat currencies. The USD (US Dollar) has a base value because taxes must be paid with it, and people are willing to pay those taxes because being a business in the US is more productive than being a business in a country like Somalia. In turn, US businesses deal in USD, so the value of US goods acts as an incentive to increase the value of the USD — if you want an American truck, you'll need to get USD. A neat example of this is OPEC who decided long ago that their oil would be indexed in USD. So the value of oil contributes to the USD's value, and since everyone wants oil, the value of oil provides a strong leg to 'prop up' the USD's value even if the US economy is doing poorly. This is why it is a financial concern when OPEC talks about switching to the Euro — it means the USD would be losing one of its pillars of value while the Euro would gain one.
So what's the value or promise of a fiat currency? Access to the economy of the country that issued it, as well as any satellites of that dollar economy.