The humerus is one of either of the long bones of the arm that joins the shoulder (in particular, the scapula) to the elbow. It's rounded at the point where it meets the shoulder so that it can move freely in the shoulder socket. It's then more or less cylindrical, and where it meets the elbow it has a triangular section.
A diagram of the humerus, courtesy Wikimedia Commons
The point where the round part at the top meets the cylindrical part is often where the bone breaks. For this reason, it's called the surgical neck.
The humerus can be moved through the widest range of any bone in the body and has such have a complicated system of muscles. The muscles attached to the humerus are the deltoid, pectoralis major, teres major, latissimus dorsi, infraspinatus, teres minor, biceps brachii, coracobrachialis muscle, brachioradialus, triceps brachii, and the anconeus. These muscles also allow the humerus to provide stability and leverage when the arms are used for lifting.
The three major nerves that pass by the humerus are the axillary nerve, the radial nerve, and the ulnar nerve. A dislocation of the bone in the socket will affect the axillary nerve as well as possibly damaging the axillary artery.