What does it mean when a 1st-level fighter takes 5 damage? That is, if observed in the game world, how would an onlooker describe the wound? Is it a vicious cut into the gut and spine, or is it just a superficial flesh wound? What if a 10th-level fighter takes 5 damage? Is the wound the same severity? What if a 10-hit die giant takes 5 damage? Still the same? Do higher-hit point creatures receive smaller wounds from equivalent damage? And why does it take longer for a high-hp character to fully heal from 1 hit point to maximum, than it does for a low-hp character?
All Gygax-era versions of D&D and AD&D share the same set of answers. There is consistent, naturalistic meaning to both damage and hit points, as implied by the various relevant mechanics...
Damage that Kills You vs. Damage that Doesn't
Creatures aren't materially affected by damage that doesn't reduce them to zero hit points. A 10th-level character might start with 51 hp, and then get hit ten times, each for 5 damage; but he still adventures at full capacity, simply by virtue of having 1 hp left. Despite receiving 50 damage (enough points to kill three average warhorses), he doesn't suffer any movement rate or carrying capacity reduction. He doesn't suffer any attack, AC, or save penalties. If applicable, he can still cast spells, or scale sheer walls using just his hands and feet.
This shows that those wounds, each triggered by 5 damage, are pretty minor.
However, characters are significantly affected by damage that does reduce them to zero or lower. If that same character subsequently gets hit for 5 more damage from an orc's sword attack, he's dead.
This shows that even though all those attacks delivered the same quantity of damage, only the last one mattered in terms of the character's capabilities.
Another example: Consider a 1st-level character with just 1 hp maximum. If he gets hit for 5 damage from an orc's sword attack, he's dead. Just as dead, in fact, as the 10th-level character. Hell, it could have been the same orc that killed them both.
This shows that when damage kills a character, neither the character's full hp, nor the attacker's & defender's relative skill are significant in describing the injury. In both the 1st-level and 10th-level cases, we could describe the sword thrust as a cut that slashed through intestines and severed ribs and spine.
Yet another example: The previous 51 hp character starts fresh, after being wished back to life. During a dungeon expedition, he gets blasted by fireball for 50 damage. He's down to 1 hp again, and of course he still adventures at full capacity.
But if he subsequently gets hit by for 5 more damage from the same orc's sword attack, he's dead.
Even though the fireball reduced the character's hp by ten times more than the orc's sword, the orc's sword attack still caused a bigger, more grievous wound.
This all shows that the biggest factor in the description of a wound isn't the number of "points" of damage, but rather: Did the wound reduce the character to zero or below? A 1 damage hit that kills you should be described as a more serious injury than a 100 damage hit that doesn't kill you.
Describing Damage that Doesn't Kill You
Whether a combatant is 1st level with 5 hp or 10th level with 50 hp, a 4 point blow that doesn't kill him represents the same amount of physical damage — a superficial laceration, a contusion, perhaps a non-debilitating fracture, etc.
Among blows that don't kill a character, ones that deal less damage represent more minor wounds, as compared to blows that deal more damage. It's not unreasonable to think that a high level fighter in a fantasy world can fight at full effectiveness despite a bone break, a slight concussion and a deep muscle laceration, each of which could be a fine description for a 15+ damage hit that didn't kill him.
But Hit Points Also Represent Skill & Luck, Right?
That idea is crudely paraphrased from the Players Handbook (page 34) and Dungeon Masters Guide (page 82). What the "skill & luck" concept really means is this:
Higher hp only represents fighting skill, luck, divine favor, and what-not insofar as it allows a character to take one more minor wound instead of a fatal wound.
After the skillful, lucky, or divinely-favored character takes some damage (and thus some wounds), his rest doesn't actually restore his skill, luck, or divine favor. His rest is really about healing actual physical wounds. (Yes, I realize this might not mesh 100% with the DMG phrase about "metaphysical peak".)
So that 5 damage wound mentioned way up at the top: If it didn't kill the recipient, it's a pretty minor wound, regardless of how many hp he has left. But if it did kill the recipient, it's a really nasty wound.
A 10th-level character who has suffered a total of 50 damage from ten different attacks really does have ten wounds. They're probably all minor, and they don't impact his active capabilities, but they're there nonetheless.
That is why high level characters typically behave differently in-game when they have greatly reduced hp (and are thus closer to zero hp). The accumulating pain of many small wounds, the trickle of blood in the eye, the weight of his shield on the arm with the hairline fracture — these are all clues to the high-level fighter that he cannot keep up fighting this way forever, and that it's time for his comrade to take a turn at the front of the party.
Hell, maybe that 10th-level character has an 18 constitution and got some great hp rolls, for a total of 100 hp or more. After a brutal day of adventuring, he may be walking around with dozens of small wounds. This is not unreasonable for someone of heroic bent and the pinnacle of human constitution.
(To be added later. This shows how the natural healing rates in various D&Ds also support the idea all damage represents actual (though typically non-debilitating) wounds. Mention also AD&D's rule about four weeks of rest being enough to restore all hp.)
This understanding of damage and wounds works together with cure spells, with a surprising amount verisimilitude. Ignore the adjectives in the cure spell names ("light," "serious," "critical"); the spell names are also game-world parlance, so just think of it as the first cleric choosing spell names that seemed pretty good, without worrying about absolute naming perfection.
Cure light wounds and cure critical wounds aren't really about the difference in severity of wounds in an absolute sense. That is, cure critical wounds will generally be used on wounds that aren't really critical. The various spells are more about lesser and greater quantities of wounds healed, relative to each other. Roughly speaking, a cure light wounds spell heals one small wound, whereas cure critical wounds heals four small wounds or one large (and yet still not debilitating) wound.
(To be added later: Note that fact that even cure spells used to bring a character back to positive hit points do not obviate AD&D's requirement for one week's rest after having dropped to zero or below.)
Damage to Giants, Monsters, and Worse
(To be added, to help understand the meaning of damage on creatures physically larger than humans.)
Falling: Where this Descriptive Model Falls Down
(To be added. Admittedly this model doesn't handle descriptions of falling damage very well. But then again, by-the-book falling damage has been tricky to fit into most/all models for the meaning of damage.)
Character Hit Points on page 34 of the Players Handbook
Hit Points on page 82 of the Dungeon Masters Guide
The Explaining Hit Points article at The Alexandrian gets it almost right for Gygax-era versions of D&D, but misses the mark on a few details (mostly by not accounting properly for the implications of healing on the description of damage):