Your weapon dmg is a random number generated on a swing in between the min and max dmg on your weapon. Attributes that increases your dmg is then factored, and it gives you the "weapon dmg" number, on which is calculated the dmg of your skill.
ex: you are a barbarian, and you do a Hammer of the Ancient. You have a 2h axe that has 11min dmg and 17 max dmg. A random number is then generated in between 11 and 17, let's say 15. Then your strenght increases this dmg to 25. Hammer of the Ancients does 200% weapon dmg, so 25 x 200% = 50 dmg.
In this case, if you were dual-wielding, Hammer of the Ancient counts weapon dmg on your main hand weapon. Cleave alternate hands, so one time if counts it on main hand, the other on off-hand.
Attack speed is not factored at all in weapon dmg, but is for DPS (Damage Per Second). Attack speed will not increase the dmg of your Hammer of the Ancients, but will enable you to spam it faster.
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ex: you are a barbarian, and you do a Hammer of the Ancient. You have a 2h axe that has 11min dmg and 17 max dmg. A random number is then generated in between 11 and 17, let's say 15. Then your strenght increases this dmg to 25. Hammer of the Ancients does 200% weapon dmg, so 25 x 200% = 50 dmg.
In this case, if you were dual-wielding, Hammer of the Ancient counts weapon dmg on your main hand weapon. Cleave alternate hands, so one time if counts it on main hand, the other on off-hand.
Attack speed is not factored at all in weapon dmg, but is for DPS (Damage Per Second). Attack speed will not increase the dmg of your Hammer of the Ancients, but will enable you to spam it faster.