There are two that I know of:

wegoshop.com and
gardengrocer.com.

They operate a bit differently, and are priced differently. You can check their websites for specifics.

In general:

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.