Two weapon fighting in 4e depends on how, exactly, you're attacking.
If you're making a basic attack, the benefit of having a weapon in each of your right and left hands is that you get to choose which weapon you use in the attack.
If you're making an attack with an attack power that doesn't specify "Requirement: You must be wielding two melee weapons.", then the benefit is the same as above.
If you're making an attack with an attack power that *does* specify "you must be wielding two weapons", then the benefit is that you get to perform that power.
So that's that.
There are a couple of feats that anyone can use, so long as they've meet the 13 Dex pre-req. Two Weapon Fighting gives you +1 damage to your main weapon when you wield two weapons. Two Weapon Defense gives you +1 AC and +1 Reflex when you wield two weapons. Taking both those feats gives you the benefit of a two-handed weapon (usually, around +1 average damage) and the benefit of a light shield (+1 AC and +1 Reflex).
I think mostly rangers and rogues will use TWF. Melee rangers have a lot of powers that require two weapons, so if they have the Dex they might as well pick up TWF and TWD. Although see my build for
Irongorn the Heavy Ranger. Rogues will not typically have the Con to qualify for shield proficiency, so TWD is attractive and the damage bonus from TWF is nice.
For example, a 2nd level halfling rogue with 20 Dex, 16 Charisma, and the feats TWF and Weapon Focus: Dagger has a deadly at-will attack, Sly Flourish, which nets out to + 10 attack (+1 for 1/2 level, +5 Dex, +1 rogue weapon talent, +3 proficiency), 1d4 + 11 damage (+5 dex, +4 charisma, +1 TWF, +1 weapon focus).
That's big damage for 2nd level, particularly if you get the drop on the enemy and add in 2d6 for sneak attack.
But I digress. The upshot is that TWF is just a fighting style; it doesn't add any extra attacks or new abilities.