ZK delivers scale, and ZK delivers privacy, and it does both by relying on a proof.
This moon-math proof is key to everything:
It attests to the validity of txs, and verifying the proof alone is enough to know that you can update the state based on these txs without having to re-execute them (that's how we get scale), and without having to see their details (that's how we get privacy).
If you want a simplified (but long!) explanation about HOW do you build such a moon-math proof, this article is for you.
Enjoy ;-)