From Dungeons of Dredmor Wiki
"What's better than one weapon? Two weapons at the very same time!"
This skill will allow the player to use two weapons simultaneously without a penalty.
 Granted Abilities
When dual wielding, the melee damage of both weapons is added together. If you have the corresponding melee weapon skill (e.g. the Maces skill for a mace), each weapon gets damage bonuses according to the weapon skill. For example, if you wield two maces ( 2 each) with the level 1 Maces skill ( +1), your total melee damage will be 6 ( 2 + 1 per mace).
You can wield two weapons without the dual wielding skill. If you do, an icon appears to the left of the screen warning you that your attacks will be less effective until you let go of one weapon.