When you bend your elbow, the Olecranon Process is the big bony bump that sticks out to the back like a pointer. In fact it is commonly referred to as the "point of the elbow". The elbow is a joint where the bone of the upper arm (humerus) meets the two bones (radius and ulna) of the lower arm. The bump of the Olecranon Process is actually the uppermost part of the Ulna. It is where the triceps muscle along the back of the upper arm attaches and pulls to straighten the elbow. When you "elbow your way" through a crowd, you are using your olecranon processes. When you sat with your elbows on the table (to your mother's disapproval), it is where your arms made contact with the table surface.

More Info: en.wikipedia.org