Lets Start With What the USD is backed by
The USD is no longer backed by gold1, but by a promise that the US Government will pay its debt (in the form of payment the interest on (and sometime redeem) government securities when due). If these payments are not made to the debt holders (Corporations, China, treasury-bond holders) then a default would occur, which would shift international use of the USD into other currencies. This would flood the US economy will low-value dollars, resulting in massive hyper-inflation.
If you remember the the “Debt Ceiling Crisis” of 2011, the “Fiscal Cliff” of 2013 (and the Government Shutdowns of 2018 and 2019)2, then i’m sure you can understand why international faith in the US Gov promise to pay its debt is wearing thin.
The USD is also backed by simple faith in that the dollar is “Just what everyone uses, so I’ll use it”. This is fine and good. Many currencies have succeeded since the early 18th century largely on faith. Faith can shift based on perceptions however, so once people begin to see that “The Emperor Has No Clothes”, they will begin to store value in other stores-of-value.
So what is Bitcoin backed by?
So basically BTC is backed by mathematics, technology and an economy, just like any other currency, but without a central bank. Some argue this is better than any other fiat currency because a fiat currency is controlled by (and manipulated by) a governing power; BTC is peer-to-peer. The block chain is the public record of all BTC transactions, in chronological order. This means that all transactions are known to the world; contrast this with how little we know of central bank activities.
Mathematics Bitcoins are created and transacted by a mathematical proof-of-work3. This means that in order to create a new bitcoin, and to conduct a bitcoin transaction; computers must provide a solution to a complex mathematics problem that takes time & electricity to compute. This creates intrinsic value in the form of time and cost-of-electricity and simultaneously verifies the authenticity of the new coins and transactions. Contrast that with the intrinsic value of a piece of printed paper of a US Dollar bill.
Economy Bitcoin is “backed” by its usefulness. Just as is the US dollar. As long as you can do things with it, then it has value. The more people can do with BTC, the more value it will have. In time, the technology and economic rules might make BTC more appealing than the USD.