The higher the number, the less light enters the camera, but the more likely you are to freeze the action in the image you are capturing. If you’re shooting a moving subject, a higher shutter speed is probably appropriate.
The lower the number, the more light enters the camera and the less likely that the entire image will be in focus. Unless you are using a tripod or your camera or lens has built-in vibration reduction, you probably don’t want to use shutter speeds much lower than 60, otherwise you risk a blurry image. However, longer exposures of say ½ a second or longer (again, using a tripod) can produce some very cool effects.