It's not parry or backstab. There's a certain amount time when an enemy is in a vulnerable position, where if you hit them, it deals extra damage. 20% normally. Vulnerable positions are mid-swing of an attack, healing, poise broken, shield broken, or from behind. This only works with weapons that have thrust attacks. Any time you trade blows with someone simultaneously, you should probably do counter damage. If the enemy's poise is low, you can cancel their attack because of "poise break." Your Gravelord Sword should be able to do that with most hollows and weaker enemies. As far as I know, the counter mechanic works for all enemies including bosses.
With the Leo Ring, you get a 40% boost to counter damage for a total of approximately 60% on top of your weapons normal damage.
The combat system is quite complex. I hope I explained that clearly and correctly.