"Bitcoin isn't backed by anything. It doesn't have any intrinsic value."

Intrinsic: "The essential nature of a thing."

Value: "Relative worth, utility, or importance"

The essential nature of bitcoin (its immutability, scarcity, fungibility, etc) is the relative worth, utility, and importance human beings find in it. Hence the reason they back it by saving in it, running the network, and protecting its ideals.