Most of the time I want my photo to be tact sharp by keeping the shutter speed nice and high, especially action shots. At times, to get a little creative you want the shutter to be slow adding a little flair to your photo. By doing so it creates the blurry illusion of movement in your images.
I am sure you have seen shots on SS that shows a speeding boat and the water around it is blurry and looks like they are traveling at great speed.
The shot is achieved by lowering your shutter speed on your camera. The camera needs to be as still on your subject and allow the other objects around it to move and blur out. When I say slow I meant 15/s to 60/s but this varies according to your lighting conditions and desire effect.
To do this you can shoot in manual mode. The easiest way however, is to set the camera on S (shutter priority mode). You then crank it down to the numbers you want. Take a bunch of photo and see which one gets the effects you want. If there is too much light to lower your shutter speed you can add a polarize filter or ND fitler to cut down some light. These filters take away light and allow you to have a lower shutter speed even in bright sun light conditions.
This is my friend Brad today. I shot this photo at ISO 200 and shutter speed 40/s. Holding the camera as still as possible and letting the sparks move and get blurry.