The number is the double-sha256 hash of the block header. Part of that header is determined by what goes in the block, but a part of it is an arbitrary number that miners can change at will, the "nonce". Miners change that number a bazillion times and do the hashing again and again until the result of the operation is a number smaller than 10^15.
Discussion
Learning this is what really blew my mind on Bitcoin the first time. The second time was when I baked my noodle on ECDSA and how that works.