Proof of Work is the original blockchain consensus method, used by Bitcoin. Participants spend computational energy to add blocks. Miners compete to solve a puzzle: find a number that, hashed with the block data, falls below a target. The work is expensive. Checking the answer is cheap. The winner adds the block and takes the reward.
Security is strong. Attacking Bitcoin means acquiring 51% of hash rate, which is costly in hardware and electricity. The energy is the cost of rewriting history. To reverse transactions you would redo all work since those blocks. Critics point at the environment. Bitcoin uses as much electricity as many countries. Defenders say that energy buys a neutral, hard-to-censor monetary network.
The argument is the tradeoff among security, decentralization, and resource use. That tradeoff is why Ethereum moved to Proof of Stake. This is computationally expensive but trivially verifiable by others. The miner who finds the solution first gets to add the next block and earns the block reward. The energy expenditure isn't waste; it's the mechanism that makes rewinding history expensive.
The criticism is environmental: Bitcoin consumes as much electricity as many countries. Bitcoin's proof of work makes a block expensive to produce and cheap to verify. Changing history means redoing that work.
Proof of Work Mining Simulator
Experience how miners compete to solve cryptographic puzzles by finding the right nonce value