The Triceps Brachii has three heads which connect the humerus and scapula to the forearm bone called the ulna. These heads are known as the Lateral, Medial, and Long heads.  The Lateral head is located on the outward facing side of the humerus. This head is most responsible for the horseshoe shape of the Triceps.  The Medial head is located towards the midline of the body.  The Long head is along the bottom side of the humerus and is the largest of the three heads.  The primary function of the Tricep is to extend the elbow (straightening the arm).   The secondary function of the Tricep is fulfilled only by the Long head of the muscle, which is to bring the arm down towards the body (adduction). The Tricep shares this function with the Latissimus Dorsi. 

Exercises that work the Triceps include Pushdowns, Seated barbell french press,  Dips, Close-grip bench press, Lying extensions etc