DR in D&D subtracts a specific number from the damage done, eliminating that damage from affecting the player. And this DR can reduce damage to zero.
Wait are you talking about the tables in ...1st & 2nd ed? where AC 8 would have -2 bonus v say a Copesh?
No. 3rd and 4th edition only as far as I know.
I think they called it immunity and stuff like that before 3rd.
Example
DR: 5/+1
That means that you reduce damage dealt by five unless you are using a plus one whatever.
Damage reduction due to specific cercumstance, Yeah, And those were usually for specific MAGICAL creatures Werewolves, Vampires & other undead, It was special case damage and it was also a set amount of damage reduction, as the example indicates.
Remember before fourth edition?
I swing at you. Miss. You swing at me. Miss. I swing at you. Hit. You take 5 damage. Your turn. Bor-ring.
Yeah, I liked those editions, before fighters could heal themselves in combat without a potion! It wasn't boring if you had 7 HP!

Yeah kinda boring like:
I shoot you, I got 6 hits
I got 4 defending
Ok so thats 6 damage from my pistol.
Ok I soak 8 damage.
Damn. Again!
Rinse and repeat!Walk away frustrated!