Dual Wielding Proper

You master fighting with two weapons, gaining the following benefits:

• You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren’t light.
• You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.
• When you make an attack action, you swing with both weapons simultaneously. If the weapons have different "to hit" modifiers, roll to hit with each sword respectively.

This, in essence, bypasses the need to use your Bonus Action to swing with your off-handed weapon, as detailed in the Player's Handbook.