You can Complete a Task with or without completing any Subtasks it contains.
From the work list, open the Task tile by selecting the Task summary. This will activate a Details Tile on the right-hand side of your screen.
If you're on a work board, open the task summary by clicking on a task tile.
From the Action Bar on the right side, the File icon will allow you to update the Status of the Task.
Select Completed and Save.
If the Task contains Subtasks, you don't have to have all Subtasks checked to Complete the Task. Likewise, checking all the Tick Boxes alone will not Complete a Task.
You will be shown the number of outstanding subtasks and be asked if you're sure you want to mark the task as complete. Click Yes or No.
The Completed Task will now appear on your Completed Items board.