Overdue items help to keep your schedule on track.  Given how the schedule can change from day to day, schedule items are NOT automatically marked complete, based on the items end date.  

If you see a red dot indicator, that means that you have new overdue items that you have not seen yet.  The number inside the overdue badge, indicates how many overdue items there are.  That number will not go away until you have addressed those items, by either marking them complete or changing the start and/or end dates.

You can update overdue items from the main dashboard or from the project dashboard.