Can you explain ZK to me? People throw that word around but I never understood what it meant. How do you prove something without knowledge?

I understand the simple interactive examples; I can prove I possess some information if I reveal calculations with that information, and they can be proven valid, such as I could convince someone I have a private key if I can decrypt enough messages encrypted to its public key.

But I don't understand the non interactive proofs, and I don't understand how you can prove the bitcoin chain for someone without ALSO having the chain.