The Attack Dog perk allows your canine companion to grab an enemy's limb in combat, increasing your chance to hit in V.A.T.S. and possibly causing additional damage as well.”— Fallout 4 loading screen hints
This three rank perk revolves around increasing the effectiveness of your canine companion, Dogmeat. The first rank allows him to hold an enemy and make it easier to hit them in V.A.T.S.. The second rank gives him a chance to cripple the limb of the opponent he is holding. The third and final rank gives him a chance to cause bleeding damage to the enemy he is holding.
With Nuka-World, a fourth rank is added, which reduces damage by a flat 10%.