Don't read 'parry bonus' as 'parry damage.' I think that's where the confusion is coming from.

'Parry' and 'damage' are two concepts that should not be conflated. No parry in this game inflicts damage. It's confusing, I know, but the parry bonus for an item helps calculate how much incoming damage from the enemy's attack you just parried gets blocked.

When you successfully parry with a shield or weapon, it often will stagger the enemy. While the enemy is staggered, you can do an attack that will inflict 2x the attacking weapon's primary attack value. Attacking a staggered enemy always does 2x damage with whichever weapon used in your attack.

To be clear, parrying will block more damage than a poorly timed block or just being in a defensive stance by holding down the right mouse button continuously. When successfully parrying, the Parry bonus of the shield or weapon used in the parry attempt applies to stop more incoming damage than you would have otherwise. The parry will also stagger the enemy, setting them up for a followup attack that will do 2x damage of whatever weapon you use in that attack.