When you have notifications they will appear in a red 'bubble' on the notification button (much like Facebook).
When you click this button you will see a simple view of your most recent notifications.
These notifications are in the pending list. To remove a notification from this list (and from the red bubble) you will need to click this notification and click 'Complete' in the bottom right corner.
This will mark the notification as completed and it will appear in the completed list, rather than the pending list.
Please note that some notifications may be old, so you may need to click 'View all notifications' and complete them within this list.