The technical term is oral prophylaxis, which means prevention of oral disease.
One way to prevent oral disease is to remove harmful plaque and tartar (calculus) both above and below the gum line. You may also be given special instructions on brushing or flossing to keep clean the areas where we found significant buildup. That is the familiar "cleaning" part of your checkup.
Teeth Whitening actually a mild bleaching process that restores stained or discolored teeth.