In D&D, zombies are slow, lumbering undead. They are created by evil magic users from the corpses of the dead. They are so slow that they attack last every round. A good cleric has a chance to turn them and make them leave the cleric and his party alone for a time. A high enough level cleric will turn them to dust instead of turning them away. An evil cleric has a chance to take over the zombies and command them. This holds true for all types of undead.

Unlike recent movies and TV shows, a wound from a zombie does not turn you into a zombie when you die. One could make the case that a corpse attacking you gives you a chance of catching a disease. They are also not brain eaters. They are merely undead used as guards and cannon fodder by the bad guys.