As far as I understand, Bitcoin is backed by energy and scarcity, much like gold: it requires significant energy to "mine" a Bitcoin, and it can't be easily duplicated, if at all. That's its intrinsic value, unlike fiat currencies that can be printed easily (correct me if I'm wrong).
I also believe that even gold has little intrinsic value, perhaps even less than steel. Ultimately, it's really a question of how valuable something is as a medium of exchange. Bitcoin is durable, portable, divisible, scarce, verifiable, and decentralized, which makes it a valuable form of currency. I suppose that's its exchange value.