Armour actually reduces intake damage which means, a hero with more armor takes lesser damage, a hero with less armor takes more intake damage (but still lesser than actual damage dealt to him)
Since in dota, armor can go negative (below zero) armor means much painful intake damage. In other words, it amplifies the intake damage.
Zero armor is straight forward, no damage is reduced so exactly same amount of damage is taken.
to give you and idea without going into much math,
Say drow and sniper are in clash
Say sniper has 10 damage and he hits drow 5 times. Now mathematically drow took 10x5 = 50 damage but its not.
Now how much drow takes damage?
It depends on how much drow's armor is
If drow has +10 armor, she takes less than 50 damage (less than 10 damage per hit)
If drow has 0 armor, she takes exactly 50 damage (10 damage per hit)
If drow has -10 armour, she take more than 50 damage, (more than 10 damage per hit)
Check Armor and Damage to know in full details and math