If order is paid by PO, check, phone/fax order or credit card with manual processing, it will come in this status. Customer will get order received notification. You can change order status manually to "P" - Processed after you've got the funds (so customer gets order processed notification).
Means you've got paid for the order but it was not shipped yet. Orders will come in this status if you are using online credit card processing via payment gateway and card was processed there. Can be set manually, customer gets order processed notification
If your payment gateway declined the credit card, order will come in this status. Can be set manually. Customer gets order declined notification.
Set manually. No notification is sent to the customer.
Set manually - means you shipped the order - customer gets order complete notification with tracking number inside (if you are using it)