The muscles at the back of the upper arm are commonly called the triceps. The full anatomical name, triceps brachii, means “three-headed muscle of the arm,” describing its three muscle heads.
Those heads are the long head, lateral head, and medial head. All three join into a common tendon that attaches to the olecranon of the ulna, the prominent bony point of the elbow. Their main job is extending the forearm at the elbow, as when pushing a door, performing a press-up, or throwing.
The long head differs from the other two because it also crosses the shoulder joint. It can therefore contribute to movements involving the upper arm at the shoulder as well as elbow extension.
The most frequent mix-up is placing the biceps at the back of the arm. The biceps brachii is on the front and primarily bends the elbow, while the triceps are on the back and straighten it. “Triceps” can describe other three-headed muscles elsewhere in the body, but in ordinary fitness language it usually means the upper-arm muscle group.