Manually selecting shutter speeds allows you to control the amount of subject (or camera) movement that is recorded in the picture.
If you want to freeze movement or emphasize it, selecting the right shutter speed is dependent on the speed of the subject, the direction it is moving in relation to the camera and how big it is in the frame.
As a guide, a person jogging head on to the camera can be recorded with a shutter speed of 1/60, while a formula 1 car traveling across the frame would need 1/2000 to 1/1000 to freeze it.
If you want to emphasize movement, you could try panning with your subject. This involves tripping the shutter while tracking the subject with your camera. The effect will be a relatively sharp subject against a blurred background. Try experimenting with slower shutter speeds until you get the hang of it and take plenty of images.
You don't always want to stop all subject movement. Flowing water for instance can be recorded by a fast shutter speed to make it look frozen or glass-like, while selecting a slower shutter speed will give it a soft almost ethereal quality.
One shutter speed worth mentioning is B (bulb) This keeps the shutter open for as long as you keep your finger on the release button and is used for very long exposures.