Same thing backing the US dollar.
At least the US dollar has ink and paper—both of which will be worth more than the face value of the bill in due course.
That's not entirely correct. The USD is backed by the enormous mass of goods and services that are ready to be exchanged for it. BTC is backed by hardly anything because there are virtually no goods or services that are exchangeable for a BTC. No merchant would want to hold the BTC, which is not a surprise considering BTC's volatility. A few vendors sell stuff "for BTC," but in reality they convert your BTC into USD and then sell you the product for those USD.