"Hardness is the new stat for weapons and armor. It determines your chance to either damage opponent's armor (reduce its Damage Resistance) or avoid being damaged. We take into account the material as well (i.e. it's easier to damage bronze armor with a steel sword than steel armor with a bronze sword). " 
Armor's DR (damage resistance) can be damaged. So for example, your 8DR armor that blocks 8 points of damage can be reduced to 6DR, etc. Damaged armor can be repaired via Crafting or Blacksmith. Weapon's Hardness increases its chance to damage the enemy's armor (as do Power Attacks, if I'm not mistaken). Armor's Hardness helps your armor resist damage. Different metals also play a role, i.e. it should be easier to damage bronze armor with a steel sword than steel armor with a bronze sword.