They deal [i]additional[/i] damage. An extra [b][u]50%[/u][/b] of your regular damage is dealt both to your primary target and other targets (very) close by. I have a Rare high-impact Hand Cannon with this perk. It deals 165 damage to a Vandal, plus an additional 83 from the explosion. That means it takes two body shots to kill a Vandal without the perk, and only one body shot to kill with it. I have no idea where these other guys got their facts, but simply playing with the perk on yields noticeable results.