Dual Wielding is the ability to use two one-handed weapons, one in each hand, as a way to increase your DPS. However, Dual Wielding imposes certain penalties to offset the damage increase.
Rogues, Warriors, Hunters and Enhancement Shaman can dual wield. Rogues can train Dual Wield at level 10, Warriors and Hunters can train Dual Wield at level 20, and Enhancement Shaman can receive the ability to Dual Wield as a 41-point talent (min level: 50).
Your mainhand weapon will deal full damage, but the weapon equipped in your offhand will only deal 50% of normal damage (although Rogues and Warriors can raise this damage with talents). Additionally, both hands will miss 19% more of the time with autoattacks. Dual Wielding does not increase your chance to miss with special attacks.
Mainhand weapons may only be used in the mainhand; offhand weapons may only be used in the offhand. One-handed weapons may be used in either hand.