There are 5 statuses that Tasks can have from the creation of the Task, to the completion of it.
Pending: The task has been created by the task manager and is waiting for you to accept it.
Ongoing: The task has been accepted by you and work is still in progress.
Awaiting review: This means you have marked the task as done and your Task Manager has been notified to review it (either mark it as Complete or switch back to Ongoing if there is still work to do). Note that you cannot change the status of the Task once it has been marked as done, only your manager can.
Completed: The task has been marked as completed by the task manager, meaning that all work has been finished. Moreover, if autogenerated invoices are enabled by the client, an invoice is going to be automatically submitted once the task is marked as complete.
Updated: The task has been updated and is waiting for you to accept the changes. Changes to the scope of a task once is has been accepted, will prompt the re-acceptance of the changes before it goes back into an 'Ongoing' status.
Canceled: The task has been canceled by the task manager.
Declined: It means you have rejected the task assigned to you.