Public Status: This determines whether or not the client can see an order marked with this status. Ie. if it is marked with a red cross then the client will not see it.
Downloads Status: This flag controls whether or not a virtual products (eg. a downloadable book) is available for download by the client at the relevant status.
This is an important flag to set if you are selling virtual products as you must make sure that you have collected payment for your goods prior to setting the order status to one with this enabled.
Other statuses that may be useful: Cancelled; Refunded; Manual Correction; Awaiting cheque/PO