What is a zero-knowledge proof, in practical terms?

A zero-knowledge proof lets one party convince another that a statement is true without revealing why it is true. In blockchain systems the usual application is scaling: a rollup executes thousands of transactions off-chain and submits a single proof that all of them were valid, so the base chain verifies one small proof instead of re-executing the work. The trade-off is that a flaw in the proving circuit is not detectable by ordinary testing, which is why circuit auditing has become a specialism of its own.