Proof of Work (PoW)
Proof of Work has participants compete to solve a computational puzzle; the winner adds the next block and earns a reward.
In depth
Miners hash the block header over and over, changing the nonce until the hash is below a target. Finding one is like a lottery — the more computing power you have, the more tickets you hold. Because the work is costly and verifiable, rewriting history would cost more than it could ever gain.
Why it matters
PoW secures Bitcoin; it is why the network has never been successfully rewritten.