Hi Cindy,
There is no real grocery store on WDW property, but depending on how
much cooking you're going to be doing, you may find what you need is
available right in the hotel gift shop.
All the resorts that have villa rooms, including the Animal Kingdom Lodge, also have mini-convenience stores
in their gift shops. The selection is not large, but you will find some
basics like milk, juice, eggs, cereal, bananas, apples, dry pasta, canned soup, a loaf of
bread, sliced cheese, beer, soda, etc. For my family's tastes, I'd be
able to find the makings of a basic breakfast or lunch there, but for
dinner I'd need another source of supplies.
To get fresh meat or veggies, you would need to rent a car or take a cab
if you wanted to visit a grocery store. Another popular alternative is
to arrange for a grocery delivery to your hotel (you don't even need to
be there when the delivery arrives.) My good friend Bret has a great
description of grocery delivery to Walt Disney World hotels.
All of the one, two, and three bedroom villas at Walt Disney World have fully equipped kitchens which include cookware, silverware, and dishes. I've listed all the
equipment in the villa kitchens in another post. (This mentions the Wilderness Lodge villas, but the Animal Kingdom is exactly the same.)
Have a wonderful vacation!