Ability Damage

is the damage dealt through any given item or weapon when using its ability.

Increasing Base Ability Damage
The skill increases ability damage by 0.5% per level, up to 30% at level 60. Increasing base and  can also indirectly increase ability damage. Base ability damage from Enchanting is rounded up.

Increasing Bonus Ability Damage
Having high and  can increase the ability damage of items in the game.

The Sheep Pet can increase ability damage from 0 to 20 depending on the level. The ability goes up by 0.2 every level. If a Minos Relic is applied to the Sheep, then it will be increased to 26 at level 100. If is then used on a weapon with ability (usually a Hyperion or Valkyrie with all three scrolls), then the ability damage will carry over to the weapon which will then be buffed by its stars inside dungeons.

The Loving reforge obtained from the Red Scarf Reforge Stone can increase by 5% when applied to a chestplate.

With 60, a Sheep Pet with Minos Relic, 5 star Wither Goggles and a 5 star Hyperion with, and a chestplate with the Loving Reforge, your ability damage will increase to 193.3 inside dungeons, essentially meaning any ability damage you do with the weapon will do around three times as much damage as with zero ability damage. Although the ability damage can be increased further by using a Superior Dragon Chestplate, Leggings and Boots, as well as the Renowned reforge on the Helmet, Leggings, and Boots, it is often not worth it as you sacrifice a lot of for not too much , which leads to dealing less damage.

Formula
$$\text{Ability Damage} = \text{Base Ability Damage} \times \left(1+ (\frac{Intelligence}{100}) \times \text{Ability Scaling}\right)$$

See table above for ability scaling