Proof of Work (PoW) is a decentralized method for randomly selecting the next block producer on a given chain.
In a PoW cryptocurrency, each transaction is broadcast to the entire network, while miners collect those transactions in blocks. As the miner’s record transactions, they are continually competing to solve its cryptographic hash and gain the reward of sealing a block. Each block begins with the hash of the previous block, creating a chain of blocks in which each transaction recorded back to the very beginning. A hash function is a conventional method for verifying the integrity of data by producing a unique string of text for any data run through it.
Producing a hash by itself is not such a challenge. However, the requirements for a Bitcoin hash are made to be very difficult, and the difficulty is algorithmically adjusted so that a new block is created around every 10 minutes. No matter how difficult it is to produce a given hash, verifying it is trivial and ensures the integrity of the data that it identifies. If even a decimal point was changed in a given block, an entirely different hash would result.
Once a miner solves a hash, they collect the block reward and broadcast the block to the rest of the network, that verifies the block, and immediately begins working to solve the next hash while collecting transactions. Occasionally, two blocks are produced at nearly the same time. When that happens there are temporarily two different chains that compete for dominance. Whichever chain produces the next block first, breaks the tie and the network follows whichever chain has the longest PoW record.
In short, PoW is the process where miners compete to solve a hash and gain a reward for block production while verifying data, recording transactions, and maintaining a complete record of each transaction back to the beginning.