They literally entitle you to pay the corresponding amount of taxes and/or fees (e.g. for market transactions) to the sovereign, which you cannot pay otherwise.
Hence why they are not mere pieces of paper with ink anymore a stock share or bond is: they're titles - the value is in what they entitle you to, not the physical substract they're on.
Bitcoin doesn't entitle you to anything other than creating a new ledger entry in the distributed ledger book that is the blockchain. Except unlike most ledger books, the Bitcoin blockchain does not record transfers of actual property between parties - it records the transfer of abstract numbers (which cannot be property in and of themselves).
Until 1971 dollars were worth something because they could be converted into one of the thousands of tons of gold bars the US stores at Fort Knox (and elsewhere).
Then a magic wand was waved over the printing presses at the US Treasury and they began to attain value for no reason. This magic has now spread to Bitcoin, Ethereum, and even cryptocoins like Dogecoin, whose creator has stated that the coin was created as a joke.
If the dollar never needed gold convertibility, why did they ever have convertibility in the first place? Why does the government spend a lot of money to store thousands of tons of unneeded gold at Fort Knox etc.?
There is a magic to the dollar - because if a panic ever causes its power to wane too much, Trump only has to utter six magical words to let it regain its power - "the convertibility window is open again".
How many thousands of tons of gold, governments, armies etc. stand behind Bitcoin?
Money has always been based more on representing debt than actually having intrinsic value (that misunderstanding comes from the barter myth, that pre-money economies had markets that used barder, which there is little anthropological evidence for - see Debt: The First 5000 Years for a pretty good overview).
As for now, the US dollar has a baseline demand because all business and income in the US requires taxes to be paid to the Government in US dollars, and all spending by the Government happens in dollars. The rest of the domestic economy emerges out of that, just as market economies always have. The value of the dollar is effectively ultimately 'backed' by the goods and services produced by the US economy. Herein lies the problem with convertibility - why would we expect that the amount of gold the Fed corresponds to the size of the economy? It won't, so the value will always diverge and hence how the system failed (more than once).