Tennis elbow causes pain at the proximal insertion of the extensor muscle group of the forearm (for the anatomy nerds, from lateral to medial: extensor carpi radialis brevis, extensor digitorum, extensor digiti minimi, and extensor carpi ulnaris.) These muscles have a common tendon that can become stressed if overused. This seems to occur with people who use hammers, screw drivers, drills as well as those who keyboard too much. Of course it can happen to those who play tennis. Ironically, I find golfers elbow more common among tennis players than tennis elbow (figure that one out...maybe this would be good for another topic!)
With overuse, there are a couple of types of stresses at the common extensor tendon that can cause issues. Rapid repetitive movements (for many months, it doesn't happen overnight) such as keyboarding can cause irritation at the tendon. Also, repetitive eccentric strain of the tendon such as hammering nails can create microtrauma causing irritation of the tendon. These types of strain are most common where the muscle meets the tendon. Prognosis for this is generally good. With soft tissue treatment, modalities such as laser, shockwave and rehabilitation using eccentric strength will significantly increase recovery time.
More excessive eccentric strain such as playing tennis can cause problems where the muscle attaches to the bone (lateral epicondyle). This is called an enthesopathy. Prognosis for this type of injury is much worse. Treatment usually involves resting from sport or activity for a lengthy period followed by treatment and rehabilitation.
Though similar in presentation, it is important to distinguish between a problem where the muscle meets the tendon, or where the tendon meets the bone so you can determine the correct course of treatment.