Could someone give me an example of how this would occur in a game? I've read it a number of times and I'm not sure how it works.

I don't have the wording with me but, whenever damage is reduced at the end of the action damge is increased by one.

So it basically cancels out toughness, and acts like armor piericing.
You have one damage and hit someone with toughness. Toughness reduces the damage to zero, Armor wars adds one. Figure takes one damage.
You hit someone with Impervious, they make thier role reducing damage to zero, Armor wars makes one stick.