"Don't expect any kind of technical answer"...? Fat chance of that here!
We aren't told what hull polarization is and how it works. We're shown what it does, though. Its protective effect does extend beyond the solid-looking hull plates, or else the blue-glowing bits of the poor NX-01 would get targeted far more often.
So let's tech. Instead of making the hull tough (this is what they do with the Structural Integrity Fields, and yes, that is a valid combat trick, too, utilized in TNG "The Chase" but probably seldom applicable and never superior to ordinary shields), the system might play with that one ubiquitous Star Trek futurotech that mankind had mastered at an early stage: artificial gravity. After installing those one-gee plates inside the
Botany Bay in the nineteen-eighties or nineties, Earth scientists no doubt experimented with higher levels of acceleration. Perhaps the hull is charged with a zillion-gee gravity field that (possibly consequently) has very short range? Not only does it stop incoming projectiles cold (we see in the likes of TNG "The Naked Now" that a force imparted on a tractor beam or by a tractor beam doesn't listen to Newton and has no corresponding counterforce), it has enough negative gravity to weaken the impact of rayguns, too. Essentially, when threatened, Archer turns his hull plates into "white holes" that are strong enough to repel even EM radiation.
This sort of push could be rigged to have a range in the order of one meter or so - see e.g. the opening credits of ST:Voyager where the ship pushes aside some swirly gases about one meter before they touch the hull. Incidentally, this would also help cover things in between the actual armor plates, such as the blue-glowing bits.
It would take a few more decades to refine this into practical tractor/pressor beams, or into featuring a "subspace trench" some distance away from the ship in which the gravitons would be dropped for the invisible zillion-gee gravity trap (which is how the TNG Tech Manual describes the combat shields of the 24th century).
So much for teching. At the practical level, the one difference vis-á-vis forcefield shields is that hull polarizing doesn't prevent transporting. Which is a
bad thing, of course, because it allows the enemy to use transporters as weapons, but luckily few of Archer's enemies realized Archer didn't have shields...
Timo Saloniemi