How "Proof of work" PoW works?

The Proof of Work consensus algorithm involves solving a computational challenging puzzle in order to create new blocks in the Bitcoin blockchain. Colloquially, the process is known as 'mining', and the nodes in the network that engage in mining are known as 'miners'. The incentive for mining transactions lies in economic payoffs, where competing miners are rewarded with 12.5 bitcoins and a small transaction fee.

As described in the 2016 Kudelski Security report,

"Proof-of-work (PoW) is the outcome of a successful mining process and, although the proof is hard to create, [it] is easy to verify."

For better understanding, please consider the following example provided by Ofir Beigel: https://99bitcoins.com/proof-of-work-proof-of-stake/

"(...) guessing a combination to a lock is a proof to a challenge. It is very hard to produce this since you will need to guess many different combinations; but once produced, it is easy to validate. Just enter the combination and see if the lock opens".

Multiple criticisms exist for the PoW consensus algorithm. PoW requires a huge amount of energy to be expended, given the computationally heavy algorithm. In addition, PoW has a high latency of transaction validation, and the concentration of mining power is located in countries where electricity is cheap. In terms of the network security, PoW is susceptible to the '51% attack', which refers to an attack on a blockchain by a group of miners controlling more than 50% of the network's computing power.

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