As mentioned before (and on the wiki) weapons have 3 different attributes that define their damage.
1. Damage type (physical, magical, fire). This is a raw number
2. Uhh damage...style? (blunt, slash, etc.)
3. Added parameters.
The raw damage is a number, the higher the number, the higher the damage of the weapon. This is important, but not that important as this number will never change unless you upgrade the weapon.
The added parameters is where the REAL damage comes into play.
Each added parameter has a rank (E, D, C, B, A, S E being the weakest and S being the strongest) that is associated with an stat (like strength, dex, luck, faith, etc.)
So, depending on the weapon, some weapons get bonuses based on your strength and your dex (like quality weapons) or other just your strength or others just your dex or other just your faith and one (1!) weapon increases with luck.
Thus, if I have a weapon with a D rating for strength and an S rating added param for Dexterity, the weapon will do a lot of damage if I have lots of dex even if I have very little strength.
Capische?