I was just thinking about this exact issue. Before abandoning the gold standard, money was basically an IOU for gold. Since abandoning the gold standard, it's clearly not an IOU anymore. It's just the value in itself. Why does it have that value? Only because we trust it.
And honestly, that's really not so different than gold. Why would the gold standard work? What intrinsic value does gold have? Again it only has that value because we trust it. If we stopped caring about gold, maybe if asteroid mining were to quickly result in 10 times the amount of gold that's currently available, gold would quickly lose that trust; same as when a government started printing money with wild abandon. As long as governments are responsible about the money supply, money is just as good as gold. But only as long as they are.
UK notes are still an IOU. The note I have in front of me says "Clydesdale Bank PLC promises to pay to the Bearer on demand Ten Pounds Sterling at their office here By order of the Board of Directors". This is one of the few cases where "legal tender" actually has meaning: if I present a wodge of bank notes to Clydesdale (or for Bank of England notes, the Bank of England) saying I want repaid in coppers, I'm obliged to accept legal tender for repayment of the debt represented by my notes. Which in Scotland means pound coins, but in England it probably means I'm getting more (although possibly different) notes back.
Interestingly, Clydesdale's office address isn't shown on the note.
Base money (both cash and central bank reserves) is often emitted through short-term repo operations. If a bank wants some base money (e.g. to put some banknotes in ATMs), it sells central bank some (usually government) bonds with promise to repurchase it after a fixed time limit (e.g. 14 days, done in periodic rounds). That is essentially a lease agreement with different legal detais.
So it is essentially an IOU for bonds, just not redeemable in retail (by individuals) but in bulk (by commercial banks). If commercial bank wants 'redeem' some cash (for bonds), then it just acquire less cash in the next round of repo operations.
It's an IOU for 100 dollars. You can exchange it for other cash IOUs from the central bank. A bank can also exchange it for electronic central bank reserve IOUs.
Now if you realize that that $100 is a mere IOU from the U.S. of A. you may get a feeling you are onto something...