Damage in general, doesn't need to be explained. If you really want a real explanation, check www.dictionary.com for definitions.

This page is about Shilla damage, generally in the form of Weapon Specialties.

When you complete one of those quests, you automatically get .5% increase in your weapon range damage. Completing all 10 quests gives you 5% So… if your weapon could do a range of between 10000-20000 points of damage, it becomes 10500-21000.

There are a few quests that specifically add damage, in amounts usually of 2%. Plus the .5%. Same formula applies.

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