Perhaps for all it is a completely different idea and representation, or simply abstraction, but for I, the concept of hit points is very much so the concept of 'not-getting-hit points', as someone else so eloquently put it. Furthermore, I like the idea of "death" at zero hit points. Lower down shall I expand my opinions.
For a hero that can't possibly become more sturdy with each level earned, the hit point, by itself is a representation and manifestation of the individual's luck, die-hard attitude, combat aptitude, and quite possibly his standing with the gods. This model goes well with the chaotic action of battle and oracular nature of the dice, and by their extension, the gods themselves. This is why fighters, followed by clerics, have better hit dice than other characters, as each demonstrates strong points in some of these elements, with backing in the others. Compare the unnatural and unlawful (in the stealing and meddling sense) ways of thieves and magic-users for why they don't fare as well. Through this angle, note I did not mention dexterity; this is a no-word. Dexterity already is used in a different abstraction known as Armour Class, or why mooks can't hit shit. Contrast with the hit points of a war elephant, or other massive and non-maneuverable beast, that is instead a value of physical fortitude.
Moving on to our other topic: zero hit points, or why I didn't cry for mommy. Completely disregarding Third Edition and newer, hitting zero hit points, as the rules read, meant dead. Now, why is that so? And how is it that if hit points measure a character's ability to avoid injury, that they're just plain out dead and dead at the total of the dreaded big '0'? Simple: it's easy to kill someone, or at least think you've killed someone. We assume here that coming with a fantasy setting is often coming with a pseudo-medieval intellect. Something often considered very ignorant by modern Man's standards (which is pretty ignorant just by thinking that). Back in "Ye Aulde Adventurre Lande", medicine and physical know-how weren't exactly up to snuff, especially after the witch hunts destroyed hundreds of years of learned healing practices, and it was very easy to mistake someone for dead, especially if the healer wasn't all that knowledgeable in their field. Clerics can cast divine healing miracles like a Pez dispenser, but they're no physician, nor paladins with their magic fingers, and definitely not the man trained solely to kill! Those thought dead may very well perish from lack of attention, infection, or simply from being abandoned by the straining and hurting party. Even a proper alkaline poison might leave ya' stone dead-ish, but not in truth. All yerr frens know is ya' failed yer damn save!
So maybe this was insightful, and maybe it wasn't. But either way it's quarter after three o' the morn'. Peace out!