Shutter Speed is simply how fast the shutter of the camera is firing at. So the faster it is, it allows the user to capture objects that are moving at a high speed.
For sport photography for example (ball related such as soccer, basketball, etc) 500th of a second is a good speed to aim for.
On the other hand to shot star trails, or streets at night where you can see the light trails, you will need anywhere from a few seconds to maybe minutes/hours of shutter speed.
However with hand held photos, the fastest I can get to is about 1/60th shutter speed, anything less than that, my shots come out blurry. This is where you would use a tripod.
Normally today's modern cameras have shutter speed from BULB mode up-to 4000th of a second.