Phone orders are requests for specific clothes from your shop. Once you get an order, you can accept it by tapping on the telephone icon. After that, you have to make the clothes requested, place them in your shop, and you will be able to deliver the order by visiting the Phone Order menu and tapping on Deliver. Note that Phone Orders don't take all of the pieces placed in your shop, so you will still be able to sell some of them.
You can earn experience, money, and fan letters by delivering these orders.