Shutters come in many different forms, and can have quite different 'travel' times over the film, from the shutter speed. However, to keep it simple, they all expose the film for the amount of time shown on the dial. Obviously, the longer the film is left exposed for, more light is allowed to fall on to the film. Long exposure times can be useful in low-light conditions, or to produce different effects. Below are two examples of the effects that can be obtained using fast and slow shutter speeds.
Notice that in the above picture (taken with 1/125th of a second exposure), the seagull in the upper-middle of the frame has been (almost) frozen in motion, since it hardly moves during 1/125th of a second.
(The above image is not the author's work and its copyright is held by a third party, used under the Microsoft clipart license)
A more artistic effect was obtained in the picture above by using a slower shutter speed of around 1/30th of a second and 'panning' with the motion of the horses. This keeps the horses fairly sharp whilst blurring their surroundings and emphasising motion.
Note that on most cameras, the shutter speed will appear as a sequence of numbers like: 8,15,30,60,125,250,500,1000, which actually represent shutter speeds that are the reciprocal of those numbers (i.e. 1/8, 1/15, 1/30... etc.).