Here are two images of what Calculus (Tarter) looks like under the gums. If you haven't had your teeth cleaned in more then two years it is possible you will have a lot of Calculus build up as seen in the photos. 

 

The Dental Hygienist will recommend a Scaling and Root Planing(Deep Cleaning) in order to remove all of it.

 

The tissue tends to pull away from the calculus because it is considered a "foreign body".This results in recession of the gums, exposing the roots of the teeth where there is no enamel.