To "wolf down" food is to eat food quickly, without fully chewing it.
Often, something that is wolfed down is not really chewed at all; it is simply swallowed.
Example: "Peter wolfed down his sandwich before leaving for work. I think he was in a hurry." In this case, Peter would have had to chew his sandwich somewhat (or choke to death!), but he did not take the time to eat the sandwich slowly. Rather, he ate as quickly as physically possible, swallowing his food in as large chunks as possible, to save time before hurrying to go to work.