It means proving something is true without providing any information other than that the information is true.

Alice wants to prove to Bob she knows the passcode to the door but without revealing the code to Bob. To do this, Bob stands outside of the cave and Alice walks inside the cave taking one of the two paths (without Bob knowing which path was taken).

Magic polynomial math over toroidal finite fields.

you will know that I know without telling you that i know

Zero Knowledge is like proving you have a secret recipe without ever revealing the ingredients.