My layman summary: Silent payments allow me to post an "address" on a public website, and someone can pay me without anyone else knowing they paid me. If that's correct, this is brilliant!
That is correct, but remember, it *only* works if the address is received from exactly once (and is marked as "spend immediately in the next transaction").
Otherwise, it just becomes a fancy method of generating a single, normal, address from a privkey, nothing else.