The damage are the amount of Life points removed from your opponent's Life bar when using Kung Fu skills. It is what you could call "physical hits". In 9Dragons, damages and wounds are not the same. Damages will display in yellow over your opponent's head when dealing normal strikes, and in red when dealing a critical hit.
Its counterweight is the defense.
It is expressed following this model: [min value]~[max value]. Those are estimated minimal and maximal damage values. Their domain will vary depending of the type of weapon used.
Attributes affecting the damage dealt
The main secondary attribute which influences the damage is your strength; it directly affects the damage dealt; one strength point gives 4-8 additional damages. The higher your strength is, the more damage you deal. Your dexterity will also modify your average damage as it will allow more critical hits.
Strength and dexterity buffs will also increase your damage.
Skills affecting the damage dealt
All active, smashing and finishing kung fu skill will cause you to deal damages when used. Some passive, rounding and charging spells will also allow you to deal extra damages.
The damage modifier provided by the skill (usually a bonus) is displayed in the skill information window, which you can get by clicking on the skill in your Kung Fu window. (S)
Items affecting the damage dealt
The main damage modifier is your character's weapon. Some weapons have a higher damage spread than others. A higher refinement level will cause a given weapon to deal more damage too, which is why refined weapons are one of the most important ressources.
Epithets role in damage
Some epithets also give damage bonuses, usually directly. Practically all killer epithets give direct damage bonuses. By giving critical rate bonuses, epithets can also affect indirectly your average damage. Those damage bonuses are expressed in absolute values, which means the damage bonus is applied to both minimum and maximum damages (1000~2350 dmg would become 1100~2450 dmg with a damage+100 bonus). It can be assumed that weapons with lower damage spread benefit more from such damage bonuses than those with high damage spreads.
Chi Kung damage is affected by many different factors than physical damage. See the approriate article.