You gain a +1 attack bonus when fighting with a one-handed melee weapon in each hand.
When you fight with two one-handed melee weapons, increase the damage you deal with missed attacks by adding your level to it. Most of your basic melee attacks, therefore, will deal double your level as miss damage.
If you fight with two one-handed melee weapons, whenever an enemy makes a melee attack against you and rolls a natural 1, you can make an opportunity attack against that foe as a free action.
One battle per day, increase the damage you deal with missed attacks to triple your level instead of double your level (from Two-Weapon Mastery).