There are some situations where you want to be sure that you are working at the same shutter speed to create motion blur or freeze action. In these cases you will want to use Shutter Priority. When in Shutter Priority you choose the shutter speed and the camera chooses the aperture. One thing you have to keep in mind with Shutter Priority is that your depth of field will change when the aperture changes. Most of the time this will not be a problem. You will have to watch that the camera is not overexposing or underexposing because it needs an aperture that is higher or lower than is available on your lens.
For example, in a situation where you are working in overcast conditions, you might choose a shutter speed that requires an aperture wider than the maximum aperture of your lens. In this situation you will need to raise your ISO so that you will not be underexposing your images. You can make sure the shutter speed you choose will work by looking into the view finder and seeing what aperture the camera will choose in your given situation. If the camera says something like “Lo” or “Hi” (check your owner’s manual for your specific camera) you will need to raise the ISO or choose another shutter speed to avoid over or under exposing your images.
To be honest Shutter Priority is the mode I use least. If I want to make sure I’m using a certain shutter speed I will head straight to Manual and set everything my self.