In much simpler terms:

Think of an IP address like a street address. 192 My Street.

There might be multiple businesses at one street address. In real life we address them with things like 1/192 My Street and 2/192 My Street, but there’s no direct parallel to that in computer networks. Instead, what we do is more like directing your letter to say “Business A c/o 192 My Street”. That’s what SNI does.

Because we have to write all of that on the outside of the envelope, everyone gets to see that we’re communicating with Business A. But what if one of the businesses at 192 My Street is highly sensitive and we’d rather people didn’t know we were communicating with them? @bjoern_tantau@swg-empire.de’s proposal is basically like if you put the “Business A” part inside the envelope, so the mailman (and anyone who sees the letter on the way) only see that it’s going to 192 My Street. Then the front room at that address could open the envelope and see that the ultimate destination is Business A, and pass it along to them.