A good definition from the PDF:

He wanted, in fact, to show that it is possible to convince without revealing, and so without unveiling his secret.

Or from wikipedia [1]:

In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true, without conveying any information apart from the fact that the statement is indeed true.

[1] http://en.wikipedia.org/wiki/Zero-knowledge_proof

I could tell you but, to trust my information, then how might you determine if I actually know what Zero Knowledge Protocols are without knowing them yourself?

If interested in the subject, I'd suggest to have a look also at DAA - Direct Anonymous Attestation [1]. It's probably one of the most advanced protocols related to ZKP, part of the Trusted Computing Group specs, there are several newer versions on pairing-based crypto, there are implementations both software and hardware... in short, it's quite an interesting protocol.

[1] http://en.wikipedia.org/wiki/Direct_Anonymous_Attestation

The wiki article should be a good start: http://en.wikipedia.org/wiki/Zero-knowledge_proof