Once a customer completes an Order on your site, and payment is made, the site will automatically set the status of that order to Payment Received.
If the item is shippable, you would normally prepare the item for shipment, print a copy of the invoice, print a shipping label from your fulfillment center (i.e. UPS), and make note of the tracking number. You should then change the status of the order to Complete.
Changing order status is not required. However, when viewing reports on order, please be mindful of the status of your orders since your Completed Orders Report will be blank if you do not change the status.