All unarmed and melee weapon attacks have a chance of knocking down your opponent. This does not affect 'automatic' melee weapons such as the Ripper or the chainsaw. The chance of knocking an opponent down is 15% while using an unarmed weapon or a one handed melee weapon, and 30% if using a two handed melee weapon.
You can knock down enemies with this perk even while they are already knocked down. Combining this with a weapon with high rate of attack can lead to situations where the enemy literally can't attack you.
Knock downs can occur on killing blows, sending the corpse flying backwards. If this happens at the same time as a Bloody Mess death, disintegrating corpses can be flung unthinkable distances and/or pushed through solid objects.
If a Melee Weapons- or Unarmed-using NPC is knocked down while blocking, due to Super Slam or other causes, all subsequent hits on that fallen character will affect them as if they were blocking.