There, I said it. I like the concept of hit points as a measure of a character or monster's survivability, at least within the context of a game primarily focused on dungeon or wilderness crawls.
I've realized that I don't really care exactly what they represent, either. Gamers agonize over it to the point of absurdity, but it's enough for me to know that they're just some unspecified amalgam of a creature's physical, mental, emotional, and spiritual vitality that keeps it going, and when they run out, either its body or spirit or both are too broken to go on, and it dies.
Yes, I know hit points aren't "realistic." That's not the point, either. Hit points make the vitality of each character, and the party as a whole, a resource to be carefully managed. In the real world, the greatest fighter who ever lived could theoretically be taken out by a stray arrow, a fall from a spooked horse, or a lucky stab from some grubby peasant with a kitchen knife. In the real world, warriors seldom just accrue nickel-and-dime wounds until they run out of health and keel over. One could enter a battle fresh as a daisy, and get cut down in the first clash. Personally, that's not what I want from D&D.
One of the most important functions of hit points in the game is to act as a buffer against the radical uncertainty of the dice, and enable a certain level of planning and strategizing that makes an adventure work as a continuous long haul rather than as a series of vignettes. In D&D, you go into battle with a pretty good idea of how much punishment you can take. You know with a fair degree of certainty whether, and for roughly how long, you can stand against a given opponent before you'll be in real danger. You know that if you have 18 hit points, you can last at least a few rounds against a couple of orcs, even if they get really lucky. That's the way it's supposed to be, because one of the major strategic elements of the game is Resource Management. You pick and choose your battles based not only on whether you think you can win, and what you stand to gain, but on how much it's going to cost you. Especially at mid and high levels, there's little chance of a character's dying in any single fight in an adventure. Instead, the entire adventure is a battle of attrition that will claim the lives of characters who squander their resources imprudently. Of course the adventure may be punctuated with intense moments of great danger, and instances where a single bad decision can mean instant death, but the very term "crawl" (as in "dungeon crawl" or "hex crawl") strongly suggests that the bulk of it is of less intensity and more strategy.
This is Combat as War. Hit points lend themselves well to Combat as War, precisely because of the resource management aspect, and their highly abstract nature. Damage subsumes not just wounds, but all the fatigue, trauma, discomfort, and deprivation of dungeon-delving and wilderness exploration. The fact that actual points of damage are usually accrued only through combat and traps is merely a point of convenience; combat and trap damage is usually a decent proxy for how much of a beating the PCs are taking from all the miscellaneous rigors of adventuring. You can judge roughly how hard a time the party has had overall by how well it has fared in the various combat encounters it has had to face.
Sure, you absolutely can construct a more specific and realistic system for dealing out combat injuries and do away with most of the abstraction of hit points. Every attack could have some chance of killing a character outright, or inflicting some particular would to some particular body part for some particular effect or hindrance. What you end up with is something which is much more radically uncertain than traditional hp-based combat.
Perhaps a more abstract analogy would make the distinction clearer. Imagine two different games of chance, each involving the rolling of a single ordinary six-sided die. In the first game, you have ten tokens and the house has only five. Each time you roll the die, you lose one token if you roll 3 or less, and the house loses one if you roll 4 or higher. You're twice as likely to wipe out the house as you are to go broke. It's still possible you could lose everything, but it's not going to happen all at once, out of the blue. If you get a couple unlucky rolls in a row and start feeling anxious, you can cut your losses and walk away.
In the other game, you and the house both have one token. Each time you roll the die, if you roll a 5 or 6, you take the house's token. If you roll a 1, it takes yours. The odds look similar, at least at a glance. You're about twice as likely to defeat the house as the house is to defeat you, (anybody with more expertise in statistics or probabilities, feel free to verify or debunk that quick and dirty assessment,) but the perceived risk is higher. There's a lot more riding on each roll of the die, and you could be wiped out all at once. Whether or not you roll again or walk away is based entirely on intuition or blind confidence, because the first round that produces a definite result ends the game.
In RPG combat, things aren't quite that simple, of course, but a game with hit point-based damage tends toward the former example, and a game with a "realistic" system of severe wounds and possible instant death tends toward the latter.
Additionally, with non-hp tracking of injuries, unless you add on some other system to track the
cumulative effects of fatigue, minor cuts and bruises, discomfort and
all that, what you have is a game in which each fight is much more a free-standing mini-scenario of its own, and much less an integral part of a whole adventure. Such a system treats a fighter
who's been tramping through a dungeon all day and fought a dozen battles as essentially equal to one who has just woken up from a peaceful
sleep in his comfortable bed, so long as their hides are intact and
their bones unbroken. In other words, as long as no serious wounds have
been taken, the party enters each fight basically fresh. I'm sure it's possible to design a system that would track a character's "energy" level separately from his significant physical injuries, and apply effects of high or low energy level to his combat ability and odds of being killed by the next attack against him, but I can't imagine it being anything other than a total logistical nightmare to run at the game table.
This isn't to say that a game with a more realistic system of combat injuries couldn't be as much fun as hp-based D&D, but it's a radical game changer.
Of course there are instances where hit points are a poor fit, too. Some styles of gaming are just made for the swingier, more radically uncertain approach like the second dice game above. A game of vignette-type encounters, in which the action cuts from scene to scene instead of crawling from room to room, probably demands that kind of uncertainty to be really exciting. I can imagine few things more boring than a series of almost certain victories in stand-alone fights.
I've also completely made peace with the idea of hit points increasing
with levels. It's just part of becoming a seasoned adventurer, and
represents not only increased combat ability, but general toughness and
tolerance for the rigors of an adventuring life. It's an amalgamation
of factors - part skill, part savvy, part plain old will to persevere,
and all the host of intangibles that separate the novice from the professional
and the merely good from the truly exceptional. Sure, you could break
it down, and try to tease out all the important elements, tracking and
applying them individually - but why? Unless it produces a hell of a lot of interesting choices and situations for the players, it's a waste of time and mental effort. Sure, there are other ways of
representing improving skill and experience, but hit points are a
perfectly good fit for a game focusing on exploration, resource
management, and Combat as War.
And besides, there are ways to inject a little more uncertainty into a hp system, without too badly diluting its virtue as a resource management element. Optional mechanics such as exploding damage dice and critical hits allow for the occasional unexpectedly lucky hit, and bolt onto the hp chassis quite nicely. "Death and dismemberment" tables (to be used either in the event of critical hits or dropping to zero hit points) provide the possibility of gruesome injuries, and again work just fine superimposed over a hit point system.