Final answer:
The shallow socket below the acromion that articulates with the humerus to form a ball-and-socket joint is called the glenoid cavity, contributing to the flexible glenohumeral joint.
Step-by-step explanation:
The shallow socket located below the acromion that forms a ball-and-socket joint with the arm bone (humerus) is known as the glenoid cavity. This joint, also referred to as the glenohumeral joint, is a multiaxial joint that allows for extensive range of motion. The glenoid cavity is only about one third the size of the humeral head but is slightly deepened by the glenoid labrum, a ring of fibrocartilage. Additionally, the articulation is supported by ligaments and a thin articular capsule facilitating movements in various directions.