The mechanics of armor class, rolling to hit, and hit points have been part of Dungeons and Dragons and RPGs from the very beginning of the hobby. They were adapted to the game from rules for naval wargames, which might explain the terminology. It makes sense to think of hitting ships, their being able to sustain multiple hits before sinking, and the quality of their armour affecting how much they can withstand a barrage of hits before sinking.
These terms have never worked very well when used for individual characters in a roleplaying game.
When first introduced, hit points were described as representing abstract qualities like skill, luck, stamina, minor cuts, bruises and scratches. This was confused by rolling to see if you "hit" a character with some sort of lethal weapon, and then seeing how much "damage" you did to them. More often than not this damaging hit with a lethal weapon left the character more or less unfazed, and they would continue to adventure as if nothing had happened.
Due to the terminology used, hit points were frequently assumed to mean how much actual physical punishment your character could take before dying. This trend towards seeing hit points as literal was underscored as videogame designers adopted the hit point mechanics from tabletop games and added a visual depiction of a character being *hit* only to reduce their hit points by some modest amount.
It's really quite remarkable how long and deeply ingrained viewing characters in the same fashion as naval warships has been for both tabletop RPGs and videogames.
The problem of course is that if someone were actually hit with a medieval weapon such that it "damaged" them, they would in all likelihood be dead or dying. Some of the videos on Spike TV's Deadliest Warrior are interesting viewing if you think a character might be able to be hit by a battle axe and walk away with some minor cuts and bruises.
Quite a few games have tried to move away from the hit points = life points approach over the years, although usually by adding a second pool of points to track or otherwise making the game more complex.
4th Edition D&D takes some steps back towards an abstract view of hit points - but it keeps the sacred-cow terminology in place, and actually makes it worse by introducing "healing surges" a term that further enforces the idea that characters are being hit, injured, and then quickly recovering.
I suppose if you want a wholly unreal and cartoon-like game you might prefer that sort of imagery of characters getting repeatedly slashed and pummeled only to keep running around like a medieval Die-Hard film... but personally it's always bothered me.
Ironically it was one of the earlier spin-off / hybrid games that I played that has the solution I'm currently finding most appealing: Fighting Fantasy game books, which used Stamina points and Luck points.
So instead of working with the legacy terminology I'm thinking of changing things a bit:
Hit Points --> Stamina Points
Roll to Hit --> Roll to Attack
Damage --> Stamina Loss
Armour Class and Healing are going to change a bit too, but that (and Luck points) are the subject of other posts...