Headcrab Zombies are Zombies from Half-Life and Half-Life 2. In Half-Life, scienctist had been turned into Zombies from the Headcrabs. In Half-Life 2, Zombies are from Citizens, but these Zombies can also throw debris at you. Zombies are usally found in non-combine locations (like Ravenholm).
To kill a Headcrab Zombie, you need to use a .357 Magnum or Shotgun. If you don't have those use your Pistol or SMG. Crowbar is ok with Zombies but you might take some damage. Really you need to aim for the head (where the headcrab is), if you aim for the lower body the Headcrab might survive. Throw debris at Zombies if you want but be careful of the suriving Headcrabs and their Torsos. Headcrab Zombies also come in Torsos. Zombies sometimes have no legs so the torsos crawl around in crouch areas like the Auto-Gun junk yard in HL2: Episode Two.