+Joshua Macy shared a post from Tales of the Rambling Bumblers about Armor as reduction.
The advantage of armor is that is distributes the force of a blow over a larger surface area than the weapon itself. The result that the force experienced by any one part of the target's body is considerably less despite the total amount of force being the same. Also note it points out why even the plate armor is not 100% effective in all cases. Not because of gaps but rather there are times when distributing the blow is not enough. A lot of time this will result in some form of blunt trauma.
Armed with this knowledge, it makes sense to represent armor as reducing damage right? That classic DnD got it horribly wrong with the Armor Class system. Well it turns out that classic DnD had a very good reason for using Armor Class in combat. It also goes hand in hand with levels and hit points.
It has to do with the game Chainmail. In Chainmail, you had man to man combat. You cross indexed the weapon you were using against the armor being worn by the target. You roll 2d6 if it equal to the target number or higher the defender is dead. In the fantasy supplement of Chainmail, a Hero could fight as four figures, and you had to deal four hit in mass combat OR man to man to take out a Hero. A Super Hero fought as 8 figures and took 8 hits to take out.
When Dave Arneson started up the Blackmoor campaign focusing on player playing individual rather than armies, his starting point for man to man combat was the Chainmail rules.
One hit = one kill was boring to Dave Arneson, so he expanded it to 1 hit = 1d6 damage and 1 hit to kill = 1d6 hit points. In addition instead having just three ranks of experience (Veteran, Hero, and Super Hero) he allowed character to be in-between those rank. A veteran+1 that could take 2d6 hit points of damage. This led to the concept of levels with the Veteran being 1st level, the Hero 4th, and the Super Hero 8th.
Gygax used this as the foundation for his draft of Dungeon & Dragons. And it was carried over the final version released in 1974. In the Greyhawk supplement weapons damage was varied in the number and kind of dice used, and each class was changed to use a different dice for hit points. (MUs and thieves: 1d4, Clerics: 1d6, Fighters: 1d8)
That what the abstraction of armor class, hit dice, and hit points means in D&D. Everything else is after the fact justification for how it evolved from Chainmail.
The more interesting question is why did it stick around for so long? There are lot of examples where trail blazer in a field is supplanted later by another that finally gets it right. But the classic D&D abstractions persist to this day and enjoy widespread popularity.