Proof-of-Work

Proof-of-Work is a system where one party proves to others that it has spent a certain amount of computational effort, in a way that is expensive to produce but cheap to verify.

Typically, the work is finding an input whose Hash Function output has some property, like starting with a certain number of zero bits. The only way to find one is by brute-force trial and error, but anyone can check the answer by computing a single hash.

Hashcash used it to make sending spam email expensive. Bitcoin uses it to secure the blockchain: miners compete to find a nonce that makes a block's hash fall below a difficulty target, and the chain with the most accumulated work is treated as the valid one. See Bitcoin: A Peer-to-Peer Electronic Cash System.