As in "zero-knowledge proof".

Let's say I need to prove to you that I know some piece of information (example: the password to a computer account, the location of your kidnapped parents) - but I don't want to reveal the information to you. A zero-knowledge proof of knowledge will allow me to do that. The phrase "zero-knowledge" arises from the fact that I can prove I know some information while providing you with no knowledge about the actual content of the information in question.

Zero-knowledge proofs are typically statistical in nature: you ask me a series of questions whose answers depend my knowing the information in question; if I can answer them all correctly, the chance that I don't know the information in question becomes negligible. Conversely, if I don't know the information, my chance of answering all the questions correctly is negligible.

Zero-knowledge proofs are covered in some detail in Bruce Schneier's excellent book, Applied Cryptography.

I expect that Zero Knowledge Systems got their name from this idea.