There are two that I know of:
They operate a bit differently, and are priced differently. You can check their websites for specifics.
At wegoshop.com, you specify items by brand name and size (UPC codes are helpful if it's an unusual item) and they shop just as you would. There is a shopping fee and gratuity added to the cost.
At gardengrocer.com, they have a standardized list. You also can request other items. I don't remember how they charge the fee--it might be a percent of the total purchase.
Both will purchase perishables as well as staples and WDW bell/luggage services will have the perishables refrigerated if you are not at the resort at the time of delivery.
If you need delivery at a very popular time (holiday weekends, for example), be sure to order well in advance to confirm your specified delivery date.