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.
Does it imply if there are multiple transaction on the address even when the sender and receiver alone knows about the transaction there is still no privacy? I was thinking if no one else knows about the transaction since it's silent payment then a strong privacy is established. I will like to know more about the "fancy method of generating a single, normal, address from a privkey, nothing else."