Consider what happens if I happen to have forgotten my mother's birthday. I meet the person who claims to know them, and I ask a 19 questions about my mother wh

Consider what happens if I happen to have forgotten my mother's birthday. I meet the person who claims to know them, and I ask a 19 questions about my mother where I know the answer, but I also sneak in the question about when her birthday is. With this scheme I use the 19 questions to check that you know my mother (that is the 1-bit of information that we are trying to prove), but with the bonus question, I get to learn something new about my mother. This shows that the proof communicated more than just the 1-bit of information. A real zero knowledge proof means that a person who is listening in on the proof doesn't glean any information either - at the end of the exchange, the only thing that has been proved is the single bit of information, and it has only been proved to the verifier. If you want a realistic example of this, then the cave example given on wikipedia is good for this. Note that at the end of the proof, an outside observer wouldn't be able to repeat the proof, nor would they even know whether the prover and verifier were in cahoots and actually just acted out the proof using a pre-agreed set of "random" choices.