A system that ties mining capability to computational power. Blocks must be hashed with an additional parameter, which requires many tries to compute a valid hash. Thus, a successfully hashed block is considered proof of computational work.
Sounds confusing? What does it actually do?
Proof-of-Work algorithms allow miners to independently try to find the next block of the blockchain. Once the block has been found, miners transmit the solution they found to the rest of the network. Consequently, the rest of the network is informed that the solution for the next block has been found, thus, they do not have to do all of the work that the miner, who found the solution, did. Thus, they only have to perform a single check that proves the solution found is legitimate.
In less technical terms, Say Bob wants to prove that he can do a really hard math question. Alice doesn’t know what the answer is, but she knows that the answer, when put through a hashing algorithm is X, thus, when Bob finds the solution, Alice only has to verify that the solution found by Bob is the solution that yields hash X.