During the Bretton Woods system, currencies were issued against gold. In contemporary times, what is the real thing against which currency is issued? What does the fiat currency actually guarantee?
Most central banks do not provide guarantees on their currency to the public. In fact it can be argued that historically they were never fully guaranteed as most central banks issued more receipts for gold (or other assets) than they had, so the receipts were never fully redeemable in the aggregate.
The American Fed was stressed during the great depression and had to go off the gold standard for the public in 1933. The international gold standard was retained and dollars were redeemable for gold for a while. This too was "overbooked" and when the rightly suspicious French started to mass redeem dollars for gold, the Americans had to get off the international gold standard as well in 1971.
Today the dollar is not redeemable for anything. You can exchange paper dollars for coins or electronic dollars, but that is just changing the form of the same thing (the monetary base).
Because you can go to jail if you don't pay your taxes in dollars, it can be said Americans are forced to purchase dollars and thus provide extrinsic value to the dollars though public tender laws (granted still different from intrinsic value but still important).
Pegged currencies are a different matter and are the closest modern equivalent to perhaps what you are asking. With a peg, a country must acquire a certain amount of an external currency to maintain a peg. It could be thought of indirectly that the country maintaining the peg is guaranteeing a redemption of their local currency to an external one. The idea is to somewhat stabilize the local banking systems which need a lot of artificial stability to survive. Granted this doesn't work well as pegs often do run out of "reserves" and suffer "runs" just like a gold standard.
Governments issuing fiat currencies guarantee only that you can pay your taxes in the currency (in fact, they tend to require that you do so). Money primarily derives its value from the willingness of others to accept it in exchange for goods and services, not from the ability to exchange it for a particular shiny metal.
There's an elaboration of the differences between the gold standard and fiat currencies at this question.
I quote some Reddit posts that answer this question more simply. I lightly corrected some writing.
Let's say that you wanted a loaf of bread from the baker. It costs 1 ounce of gold. You don't have any gold. A man comes up to you and says I'll give you 5 coins if you give me your shoes. You ask "what are these coins worth?" He says "These coins represent the 500 ounces of gold I owe you. Just bring it back to me sometime to get your gold." You ask him "Do you really have 500 ounces of gold?" He says "No".
As you laugh and are about to give the man his coins back, the baker comes over and says "Oh hey, I saw you looking at my bread! Would you like some? You can pay me with that coin!"
Would you use that coin to get your bread?
Of course you would. As long as you know that your coin is good for this exchange, you don't care what it's backed up by. All you care about is its perceived validity and wide acceptance as an exchangeable object.
If people keep accepting it as trade, that's all that matters. No matter what the reason is. If they think it's as good as the gold that doesn't really exist, that's the end of the discussion.
Why would the baker accept the coin as payment for the bread then? Because he thinks he can give it to someone else in exchange for something else. And around and around and around we go.
It's all an illusion, but it's necessary, and it works. We all just have to keep playing along, and everything will be fine.
If anyone refuses to play along, however, and tries to cash the coin in....
Well 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 and 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 thats too soft to be made into tools and frankly pretty 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 there was a known means of cashing them out into something of true value (by trading with the lord of the castle) in the event that they couldn't find someone that would accept them as a currency.
Of course once there is more than a certain amount of gold coins in circulation they in effect become a fiat currency, because the lord of the castle can only trade for so much gold before they 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 lets imagine a different kingdom. This kingdom has fertile land and is protected from invaders because of the wise policies of the king. As a result 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 kings 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 will need to obtain the paper its citizens value, which only makes the paper more valuable.
What I've just described is most fiat currencies. The 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 US dollars, so the value of US goods acts as an incentive to increase the value of the dollar - you want an American truck you'll need to get American dollars. A neat example of this is OPEC (the organization of oil producers like Saudi Arabia, Kuwait, Iran, etc) who decided long ago that their oil would be indexed in US dollars. So the value of oil contributes to the value of the US dollar, and since everyone wants oil it provides a strong leg to 'prop up' the value of the dollar even if the US economy isn't doing that well. This is why it is a financial concern when OPEC talks about switching to the Euro - it means the US dollar would be losing one of its pillers of value while the Euro would gain one.
So the value or promise of a fiat currency is access to the economy of the country that issued it, as well as any satellites of that dollar economy.
But why the US dollar (or other strong global fiat currencies) are a safe store of value hasn't been much discussed, so I'll try to change your view that way:
The US dollar is the only legal tender for US citizens to use in paying their debt (i.e. taxes) to the Federal Government.
The US still boasts the largest and (arguable) strongest economy in the world. Our financial sector and our media/entertainment industries are unquestionably the 'best' in the world - our citizens and the global community aren't going to stop trading on Wall Street or consuming our movies, TV shows, and music any time soon.
Every American who works in the largest economy on Earth is required, by law, to pay their taxes in US dollars. You could start a business tomorrow, only accept and pay your employees in Bitcoin or gold or free goods but (when April 15th comes): your taxes will be due in US dollars. Same goes for every businessperson and employee in the country.
So, Americans will keep the dollar afloat: what about the rest of the world? Well, America still boasts the largest military in the world, and has shown no compunction in using it to defend its economic interests. A big part of 'spreading democracy' is keeping recalcitrant parts of the world open to US cultural exchange and global (read: US) free trade. The very fact that we can use trade and economic sanctions as a disincentive to foreign belligerence (as we're doing now with Russia) says that losing access to American investment and American trade at least should be a major disincentive to behave in ways that America doesn't approve.
At least at present, countries and international investors are lending to the US Treasury at negative interest rates. If you lend the US government \$100, you're getting around \$98 back after 10 years. Why would anyone do this? Because you can be as close to 100% sure as possible that, after 10 years, you're getting that \$98 back. By contrast, you could take any other investment and get $150 or you could get \$25 (or nothing). The US, as a global super-power with the most powerful military on earth and the largest economy, is the safest store of value available. Better to take a small, predictable loss than an uncertain gain.
All of this leads to another point that opponents of 'fiat currency' fail to grasp: everything but consumable goods is fiat currency. Gold has no value, except in the production of semiconductors, and you can't eat semiconductors. Bitcoin, though it might not be endorsed by a government, only has value because people have decided it has value. The only things that can be truly said to have value in this world are the essentials of existence - food, water, clothing, shelter, and fuel. The second you convert those resources into any type of abstraction (be that fiat currency, precious metals, cryptocurrencies, etc.) you're created an artificial store of value. At that point, your 'currency' is only worth what people will take in exchange for it - nothing has a set value.
The US dollar has value because, if you try to block its use, you're denied access to the largest capital market, the largest entertainment market, and the largest and most active consumer market that planet has ever seen. The most powerful military force in the history of mankind will come down with the fury of God on your ass if you do anything that would challenge the dollar's global supremacy. You can say what you want about the 'rightness' or 'fairness' of this system, but Washington DC will be in ashes before the dollar loses its value, and (at that point) we'll all have a lot more to worry about than the value of our money.
The dollar (or the Euro) may collapse, but they'll collapse after their governments. And, if the governments of the most prosperous and stable countries in the history of globe collapse: God help us all. I won't be scrounging around for gold or Bitcoins: I'll be looking for tinned soup, bottled water, and bullets.
That's not quite the idea of tax-driven money. A currency is worth something when people will offer real output--goods and services--in exchange for it. By imposing a tax obligation that can only be satisfied in a specific currency the issuer creates demand for that currency motivating people to offer goods and services to obtain it.
The more people offering output for sale in a given currency, the more it can buy, the more it is worth. The USD for example is worth a lot because it's attached to a very rich underlying economy that produces a lot of real output for sale in USD. A currency attached to a smaller, less productive economy is going to be worth less.
So it's not to say the more government taxes, the more a currency would be worth but that taxes are how the worth of a country's productive output is attached to a specific currency. How much taxation is actually needed to achieve that end will vary depending on the stability and credibility of the issuer.
An already firmly established currency from a long standing stable issuer like the USD can maintain with relatively little taxation. At the other end of the spectrum a fledgling government introducing a brand new currency to a small, open economy may find it necessary to have a lot of broad and very direct taxes to drive usage. To the extent the government suffers from a lack of legitimacy or otherwise can't effectively tax, its currency will struggle to take root.