A cryptographic proof that a statement is true — this user is over 18, this batch of transactions is valid — without revealing the data behind it.
It solves two problems at once: privacy on a public ledger, and cheap verification, since checking a proof of thousands of transactions costs far less than re-running them.
We use zk mainly through proven rollups and identity providers. Writing custom circuits is a specialist, audit-heavy undertaking and we say so rather than quietly taking it on.