Remove ads by subscribing to Kanka or enabling premium features for the campaign.
When you take the Attack action and make a special attack (like a grapple or shove) using one hand, as a bonus action you can make one additional weapon attack using a melee weapon with the Versatile property that you're wielding in the other hand. You make the weapon attack with one hand on the weapon, even if you still have a free hand.
Improvement to the Extra Attack (2) / (3) feature
If you have the Extra Attack feature and with it you can make three or four attacks with the Attack action, when you engage in Versatile Fighting you can make two additional weapon attacks instead of one.
In addition, when you make an opportunity attack or an attack with the Ready action, you can engage in Versatile Fighting, but you can only make one additional attack.
If (somehow) you have a weapon that is both Light and Versatile, you can only engage in either Two-Weapon Fighting or Versatile Fighting once per standard action.