When you fight with two weapons, you gain the following benefits:

You can add your ability modifier to the damage of the additional attack.
When you make an additional attack because you are wielding two weapons (see the rules for fighting with two weapons), you can make that attack as a bonus action when you wield any one-handed weapon and you can make that attack without having to spend a bonus action if the one-handed weapon has either the light or the small size property. You can still only make this extra attack once on each of your turns.
When you make an opportunity attack wielding two melee weapons, you can make two attacks as part of the opportunity attack if the target is within both weapon’s reach - one with each weapon.