A zero-knowledge proof is a cryptographic method for convincing a verifier that a specified statement is true while keeping its private supporting information hidden. That supporting information is called a witness. The statement and any designated public inputs may remain visible; “zero knowledge” does not mean the verifier learns nothing at all.
What the proof establishes
The prover uses the witness to generate evidence that the verifier checks. Completeness means an honest proof of a true statement is accepted. Soundness limits the ability to pass off a false statement as true. The zero-knowledge property prevents the proof from revealing additional witness information beyond the public statement.
For example, a system could prove that a signed credential meets an age threshold without disclosing the birth date. The credential issuer and the rules encoded in the proof still matter. Blockchain uses also include private payments and verification of computations performed elsewhere.
Privacy is an application choice
Proof systems differ in computational cost, proof size and setup assumptions. Some require a trusted setup; others do not.
A proof establishes only the encoded claim under the system's assumptions. Incorrect constraints or implementation bugs can undermine it. Public transaction details and network metadata may still reveal information, so using ZK technology does not automatically make an application anonymous.