Each planet in our Solar System orbits the Sun in an Elipse, with the Sun occupying on of the ellipse’s Foci.
What’s in the other focus?
Nothin’.
Not a very exciting answer, but it’s just an abstract geometrical concept.
Space and lost of it.
A mathematical entity of point.
Cosmic dust?
An occasional meteorite?
Passing planetary probe?
What? Me worry?
Right, nothing.
Besides, the “other focus” is in a different position for each planet. They aren’t stable points where you can put something and have it stay.
It’s also interesting to realize that although the shape of an ellipse is symmetric about its minor axis, an orbit isn’t. The planet spends more time on the half of the orbit away from the sun than on the half of the orbit near the sun.
Nitpick: Actually the the center of the Sun isn’t “at” one of the foci. The center of gravity of the two is at the foci and both the Sun and the planet mutually orbit that point. For small little rocks like Earth is really doesn’t matter much, but for Jupiter is creates a noticable effect that has to be taken into account for advanced astronomical calculations. Okay, still inside the body of the Sun.
Ditto the Earth/Moon which is an even greater proportional offset given the closer relatives sizes of the bodies. Get two bodies closer in mass, the center of gravity won’t lie within either.
Here’s a good webpage about ellipses:
http://www.1728.com/ellipse.htm
Not to mention that it’s possible to describe ellipses with reference to only one focus. The procedure is similar to the familiar description of a parabola, that is, a focus and a directrix.
But I guess that just begs the question of what is found along the directrix…
Actually, I think the point about Jupiter and the sun rotate is just outside the surface of the sun.
The sun is about 1050 times heavier than Jupiter and the distance between them is 438,000,000 miles. If you do a moment computation the distance to the balance point from the center of the sun is 460,000 miles which is more than the radius of the sun.
Bad Astronomer?
No offense to Phil, but I’m not a bad astronomer, just a regular one (I hope.) 
The formula for the distance from the Sun to the center of mass is x=A*(m/(M+m)), so the center of mass of the Sun-Jupiter system is 740,000 km from the center of the Sun. The radius of the Sun is 695,000 km, putting the center of mass just outside the Sun’s surface.
Saying a planet orbits the sun is good to first order.
Saying it orbits the barycenter of the planet-sun system is probably good to second or third order.
But if you want to be totally precise, there are tidal effects, GR effects, and, most painfully, the fact that the Solar System is really an N-body problem - nothing orbits in an ellipse.
Oops, my memory of such calcs on the center of gravity of Sun-Jupiter was that it was still inside the Sun. Thanks for the corrections.