The forums can notify you of new content two ways. Via email or via "on site alerts". The number in the green dot is an on site alert.
The number indicates the total number of alerts, private messages, or notifications with new content. Click on your name in the navigation bar and a drop down menu appears allowing you to see how many of each type of "alert" you have, Click on the various types of alerts in the drop down menu and it will clear those items from the total in your green dot.