Armor piercing allows to ignore a % of armor allowing a small extra amount of damage. Rogues and warriors have passive buffs with piercing. All classes have skills to Piercing almost all of enemy armor.
It's not something to worry about to much. The Blacksmith will give a 20% pierce when maxed and gems will add 0.5% per level. Weapons have additional piercing as well as some trinkets and the void demon mutation.
It was mentioned that in an upcoming update that gives piercing the ability to penetrate resistances . The issue was raised by players because effectively unkillable tanks being used in brawls. The rate of pierce is 10:1 where 10% pierce will penetrate 1% of all resist types making it possible to do at least small amounts of damage.