A zero-knowledge proof is a cryptographic method that allows one party to prove to another party that they possess a piece of information without revealing that piece of information or anything about it.
Zero-knowledge proofs are often explained using Ali Baba’s Cave. Imagine there is a ring shaped cave with a door at the far end. The door can only be opened by those who know the magic word. Now, Peggy knows the magic word, and wants to prove that fact to Victor without revealing the magic word or anything about it. Let’s label the two halves of the cave A and B. Peggy chooses to enter the A half or the B half of the cave, and Victor cannot see which. Once Peggy is inside, he chooses which half she will exit from. If Peggy knows the password, she will always be able to exit from the half requested by Victor. If she does not know the password, she will only be able to exit using the requested half 50% of the time.
One use of this technique is with Layer 2 solutions. zkRollups aggregate transactions on Layer 2, and then prove to Layer 1 that they have those trades using a zero knowledge proof.