Proof-of-work as used in Bitcoin relies on finding low hashes, in other words finding hashes that begin with a certain number of zeros. To find a hash whose binary representation starts with 30 zeros, you would need to do, on average, 2^30 attempts. When you find this hash and present it, it is a proof that you have actually done about as much work. And it works both ways, when you perform 2^30 attempts, the lowest hash you will end up with will start with roughly 30 zeros.
Importantly, this works on any scale. The smallest block hash I could find starts with 23 hexadecimal zeros, or 92 binary zeros, which shows that the network has calculated around 2^92 hashes in its existence.
If you want to see it even more intuitively, check out this answer from a different thread that shows how the number of zeros in the lowest ever hash has been rising over time.