It's an injury of forearm tendons where they attach to your elbow.
You don't have to play tennis to get it. Any exertion greater than
what your forearm is capable of may cause it. Examples include opening
a jar, pitching a baseball, bowling, and carrying heavy luggage.

There are two types: forehand and backhand.

The only treatment is to rest until you can once again move your
forearm and wrist against resistance without pain. There are
exercises, but you shouldn't begin them until all pain is gone.
Ignoring the pain and exercising anyway, will cause permanent
injury.

This month's issue of "Consumer Reports" includes a review of tennis
rackets and that includes a side-bar article on tennis elbow.  I don't
have it handy, but I recall they said 95% of all cases of tennis elbow are
_not_ caused by playing tennis.

I blame most of my case on the mouse attached to my keyboard.  My doctor
gave me a bag of Lodine (anti-inflammatory, anti-pyretic, analgesic) and
recommended I sleep wearing a wrist brace.  Beyond that the treatment
seems to be "Don't do that." (-:

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I had an attack of te last year, with severe pain in the outside of the
lower right arm. There's a small depression  in the bones making up
the elbow, on the outside: if you push there with a finger it hurts
like hell if you've got te, as that's where the tendon has become detached.
Cure: complete rest of the arm for several weeks, especially no twisting
motion of the forearm relative to the upper arm. If that doesn't work,
immobilisation with a bandage or cast: if that doesn't work, surgery to
reattach the tendon.
In my case, I was 'cured' (the '' is because it can always reoccur) with
immobilisation. One point is that having your elbow strapped up transfers
rotational loads to other parts of the arm, so after a few days the
wrist and shoulder also hurt. But that's better than surgical intervention
(which is also followed by weeks of immobilisation).
RaF