A "zombie" is a dead body, or living body possesed by a virus of some sort. Zombies crave human or live flesh for some reason and the virus can be spread by either airial or physical contact or both. Airial means that you have to only breath in the exhales breath of a zombie, when physical contact means that you must only make contact, through touch, kiss, bite, ect. Zombies can die but aren't brought back by the virus because no one cares about that sort of detail.
Zombies can also be the undead. And what the first person answer is also correct, and Zombies can be killed with a single headshot with any type of caliber.