You can use task status in the task list for your own internal tracking of a task's status. A task's status changes to "In Progress" automatically when you save a translation in the Translation Workbench. In addition, it changes to "Exported" and "Imported" when those events occur. You can also change a task's status manually (except that you cannot manually change the status to "Exported" or "Imported").
Changing the status of a task through this dialog box does not change the task itself in any way. For example, changing the task status to Completed does not complete the task and forward it to the next step in the workflow, it simply indicates that you are ready to complete the step.