The triceps are a muscle with three heads, hence the name. Those heads are the long head, lateral head, and medial head. The triceps are traditionally considered a powerhouse due to their overwhelmingly fast twitch. This expression refers to muscle fibers which expend energy quickly, and the triceps are particularly dominant in this trait. The triceps are involved during any pushing movement.
The long head of the triceps originates at the scapula and inserts into the ulna. The long head extends the elbow and also assists in shoulder extension (drawing your upper arm backwards). Because the long head of the tris acts on the shoulder joint, it is preferentially recruited over the other parts of the tris when the shoulders are in flexion (arms above your head).
The lateral head of the triceps originates at the humerus and inserts into the ulna and forms the outer portion of the triceps. Along with the long head, the lateral head gives the tricep the horseshoe appearance. The lateral head has one function which is the extension of the elbow.
Just like the lateral head, the medial head originates at the humerus and inserts into the ulna. However, the medial head is hardly visible to the naked eye. The majority of the muscle sits beneath the lateral and long heads. Only the very bottom (close to the elbow) portion of the medial head is visible. The medial head, much like the lateral head, is responsible for elbow extension.