Food banks serve as suppliers to hunger relief agencies such as food pantries and soup kitchens.
If you look at food banks from a business standpoint, food banks serve as a wholesaler. They are able to acquire whole truckloads of food and distribute it in smaller quantities to agencies that serve the hungry directly. Most agencies would be unable to handle a full truckload at once, and most large donors only want to donate full truckloads at a time. In this way food banks provide a service to both donors and hunger relief agencies, meeting the donors need to move the product, and allowing agencies to receive a variety of foods in smaller quantities. This supports the cost of operating their facilities.