What do hit points physically represent?
They don't. That's my point. They don't actually have any tie to physical reality. They are a mechanical construct that is almost purely abstracted. Especially the very last one.
A minion (the usual go-to berserk button for critics of 4e) is simply making that abstraction easier to use. It recognizes that, for a sufficiently high-level character, it's merely a matter of "did you hit or not?" for whether the creature in question survives. Hence, rather than bothering with the time-draining bookkeeping (which so many old school fans claim to hate!) of checking every target's HP and keeping tabs on all this crap, you just simplify the abstraction from "this is roughly how many hits this creature takes to die" to "this creature only really needs one solid hit to die, but solid hits aren't as easy as glancing blows."
There is still a concrete reality. When we use mechanics, we are necessarily dealing with an abstraction. We should make that abstraction serve us, not the other way around.