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%. Increasing base and  can also indirectly increase ability damage.

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 50 depending on the level. The ability goes up by 0.5 every level. If a Minos Relic is applied to the Sheep, then it will be increased to 66 at level 100. If is then used on a weapon with ability (usually a Hyperion with three scrolls), then the ability damage will carry over to the weapon which will then be buffed by your Catacombs level and stars inside dungeons. Due to this, Minos Relic as well as Chimera Books are in extremely high demand, selling for many tens of millions of coins each.

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

With Enchanting 60, a Sheep Pet with Minos Relic, a Hyperion with Chimera 5, Catacombs 50, and Loving chestplate, your ability damage will increase to inside dungeons, essentially means any ability damage you do with the weapon will do more than three times as much damage as with zero ability damage. Although the ability damage can be increased further by using full Superior Dragon Armor as well as Renowned reforge on the Helmet, Leggings, and Boots, it is often not worth it as the intelligence loss from not wearing a set with a lot of intelligence is not worth it for the extra bit of Ability damage.

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

See table below for ability scaling

Trivia
's name might be a reference to "Ability Power" from the game League of Legends