There are a few reasons to use a slow shutter speed on fast or slow moving objects.
In sports like Formula One it is a great technique to visualize the actual speed. If you use 1/1000 sec on a race car it almost looks like the car is parked on the track. If you pan the picture on a slow shutter speed the actual speed of the race is a lot more visible.
Another reason for using pans is simply to get a more “creative” image of an originally boring or ordinary moment. Using a slow shutter speed of a company CEO walking into a news conference is often a better illustration than a “talking head” shot.
The most important aspect to creating a nice panning picture is the right movement with your camera. If you follow an object too fast you will not “freeze” the essential part of the picture (like an athlete, car etc…).
I usually play around with different exposure times. New lens technologies with image stabilizing programs help keep the image sharp but it is still important that the photographer does not move the camera vertically while following an object on a horizontal plane. If you move both ways the image will look shaky and most of the time its not usable.