Proof of Work or PoW is defined as a process for achieving consensus and building on a digital record known as a blockchain. With PoW, users compete with each other via their computers to solve a puzzle.
Imagine the blockchain as a digital book of records. Every page in that book can only store X amount of information. So we create new pages to store more information. Those pages are blocks in the blockchain. And creating new blocks, recording and verifying information is all a part of mining.
With Proof of Work, computers compete to solve a tough math problem. The first computer that does this is allowed to create new blocks and record information. Because mining requires computer power, people do this work in return for money. The first computer to solve this problem can record information earning them a reward in brand new digital money plus fees paid for each transaction.
Proof of Work systems are used for cryptocurrencies that regularly create and release their coins, unlike in Proof of Stake systems that have all of their coins released in the beginning.