There are lots of different types of zombies, but the one constant is that they used to be dead, and now they're only sort of dead. They're typically hungry for human flesh, in particular the brains. But they usually give up and move on after only a bite or two leaving the person they're eating to die and turn into a zombie. If they weren't such picky eaters, they'd just eat each other, and the zombie plague would sort itself out pretty quickly. But no, they only like fresh human flesh.