"Tennis elbow" is a common term for a condition caused by overuse of arm, forearm, and hand muscles that results in elbow pain. You don't have to play tennis to get this, but the term came into use because it can be a significant problem for some tennis players.
Tennis elbow is caused by either abrupt or subtle injury of the muscle and tendon area around the outside of the elbow. Tennis elbow specifically involves the area where the muscles and tendons of the forearm attach to the outside bony area (called the lateral epicondyle) of the elbow. Your doctor may call this condition lateral epicondylitis. Another common term, "golfer's elbow," refers to the same process occurring on the inside of the elbow -- what your doctor may call medial epicondylitis. Overuse injury can also affect the back or posterior part of the elbow as well.