Proof of work is the most popular consensus mechanism to validate transactions (and thus to reach consensus) in a distributed ledger system. With the proof of work no central authority is needed . The transaction is validated as soon as at least 51% of the miners have confirmed its correctness.
The mechanism is based a cryptographic puzzle. The aim is to produce a nonce for a valid Block. The miners must compute a large number of hashes until a winning hash is produced. Finding a correct solution requires a lot of computing effort, but the solution can be easily verified . For the expended power, the miners receive a reward in the form of coins.
Bitcoin uses the proof of work with the computation of the hash with a certain difficulty level, called the hashrate.
 Karzel, D., Klinger, P