Shutter speed is simply a measure of how long the camera's shutter is open for. It typically ranges from anywhere around 1/1000th of a second (a fast shutter speed or short exposure time) to several seconds (a slow shutter speed or long exposure time).
Obviously, the longer the shutter is open for, the more light reaches the camera's sensor, and vice versa.
Try to understand
Shutter speed is a much simpler concept to understand. It's basically how long the sensor/film in the camera is exposed to light. How long the shutter stays open depends on how much light there is. For pictures with the same aperture setting, if the is shutter open too long, the picture will be too bright, and if it's not open long enough, the scene will be too dark. Therefore, you control the overall exposure (lightness and darkness) of the scene with both the aperture and shutter speed control.
Your camera judges this for you, but you can manually set it as well. The shutter speed is the other (usually larger) number that isn't the aperture value. This number is actually a fraction, so if you see a shutter speed of 4000, it's actually 1/4000th of a second, while a value of 200 is 1/200th of a second. Now, remember how I mentioned stops in the aperture section? Well, they also apply to shutter speed, but in a slightly different way. By halving the time of exposure, you're letting in half the amount of light (so if you go from 1/2000 sec to 1/4000 sec, then you're letting in half the light). The opposite is true for doubling the exposure time.
What you can do with shutter speed is freeze motion with a fast shutter speed or capture movement with a slow shutter speed. Flowing water looks silky smooth at speeds slower than 1/8th of a second (with a tripod), while you can freeze water in time with fast shutter speeds. The same thing goes for hip hop dancers.
Also, an important side note is that there is a rule for getting sharp images: 1/focal length. So if you have a 50mm lens then you'd need at least 1/50th of a second for your picture to not be blurry, and if you're using a digital SLR then there is a crop value (minus a few exceptions) of 1.5/1.6 so your 50mm lens is a 75~80mm lens, which means that you need a shutter speed of at least 1/80th of a second to get a sharp image.
Summary: Fast shutter speed = freeze action. Slow shutter speed (w/ tripod) = silky flowing water.