An order status can be assigned in various ways. Some of these are manually controlled and some are updated via your merchant and shipping accounts.
Complete - This status means that order is crated, paid and shipped to customer.
Canceled - This status is assigned manually by you or, on some payment gateways, when customer does not pay within the specified time.
On Hold - This status can only be assigned manually. You can put any order on hold.
Processing - this order has been invoiced. If you use 'Authorize and Capture' payment method (or similar), invoice will be automatically created and this will be actual status for new orders.
Pending Payment - This is the status used if order is created and PayPal or similar payment method is used. This means that customer has been sent to payment gateway website but no return information has been received yet. This status will change when customer pays.
Suspected Fraud - This status is assigned when your merchant account marks the transaction as fraud.