The Dual wielding skill is a class skill that Rogues, Fighters and Salvagers start with. This skill allows you to use two one handed weapons in combat.
Any class can equip two one handed weapons however only one weapon will ever work in combat if you do not have the dual wielding skill.
The left hand weapon is the primary weapon regardless of if you have the dual wielding skill or not. If you do have the dual wielding skill then you will find that your right hand weapon is used 30% - 50% of the time.
Hitting with both weapons deals more damage over all than hitting with one weapon.
Dual wielding does not give any experience bonuses but as you are hitting with two weapons instead of one you may find your weapon skill goes up faster and you can alternate your weapon skills by having two different types of weapons equipped such as a Sword and an Axe.