If you have a manually adjustable camera, you can make identical exposures -- getting the same amount of light on the film -- using a variety of combinations of shutter speed and lens aperture, because there's a one-to-one relationship between the two.
If your light meter suggests a setting of 1/125 of a second with an aperture of f/8, for instance, you can duplicate the results at the next-faster shutter speed (1/250) and the next-larger aperture (f/11). What's the advantage of being able to choose among these combinations? Basically, there are two.
First, by choosing a combination using a fast shutter speed (say 1/500 second or faster), you enable the camera to "stop" or freeze fast action: suspend a baseball in mid-flight or a water skier coming up off a ramp.
On the other hand, choosing a combination using a slow shutter speed (say 1/30 second or slower), lets you "blur" action: You can turn a babbling brook into a slurred brushstroke of color and light, accentuating the movement of the water.
Where stop-action photography isn't at question, you can choose a small aperture (opening) of, say f/16 to produce great depth-of-field -- the area beyond and before the subject which appears to be in focus. Conversely, a wide aperture (say, f/2.8) lets you decrease depth-of-field to the point where nothing is in focus except the subject, so you can blur out distracting backgrounds and foregrounds and get a stronger picture.
Fully automatic or very basic non-adjustable cameras, don't give you the control over stop-action and depth-of-field that you have with a manually adjustable camera. But understanding the relationship between shutter speed and lens aperture is still important: Knowing that your camera's sole shutter speed is a slow 1/30, you can pass on that action photo -- it will just be a waste of film.