For instance a zkSNARK as used in ZCash. It's just a piece of data that's put there on the blockchain. It's "non-interacrive" (a term I heard, not one I made up) in that no challenges are made on it by those verifying transactions. It just encapsulates the necessary evidence all on its own. Even though I roughly understand the interactive sort of zkp, this still blows my mind.
Thanks for the link, I'll check it out.