While the Status of the Order will change with certain events e.g. payment, you can set a custom Status to appear next to the order via the Notes / History area, when viewing the Order.
Changing the Status will allow to to search/filter orders via the status, and will show theupdated status in the Orders list and detail.
Where to manually change the Status of the Order
When viewing the Order - you can change the Status via the Change Status (Ordered) dropdown in the Notes/History section.
Changing the Status will log the change in the Notes area.
Custom Order Status labels
If using the Job Status Manager plugin, you can create your own Order Statuses that will appear here.