Zero-Knowledge Proof
A method of proving a statement is true without revealing the information that makes it true.
A prover produces a proof that a verifier can check without learning the inputs, and the modern constructions used in digital assets are also succinct, meaning the proof is small and verification is fast even when the underlying computation was enormous. That succinctness, rather than the privacy, is what makes these proofs central to scaling: a contract can verify that a batch of thousands of transactions was executed correctly without re-executing any of them. Some SNARK constructions require a trusted setup ceremony whose secret must be discarded, while STARKs avoid that at the cost of larger proofs. Privacy uses do exist, including shielded transfers in Zcash and credential systems that prove an attribute without disclosing the underlying document.
In practice
A shielded Zcash transaction proves that inputs and outputs balance and that the spender was authorized, without publishing the amounts or the addresses involved.
The common misunderstanding
Zero-knowledge does not automatically mean private; most rollups use these proofs for compact verification while their transaction data stays fully public.