The ISO is light sensitivity. It controls how sensitive the camera is to light, changing it can either give a low, good, or high exposure. Having a low ISO is good in a very bright setting as it is able to darken the picture, however having it too low will lead to an underexposed picture which will be very dark. Having a high ISO is good in dark situations when you need to brighten an image. However, having a high ISO comes at a price, noise. Noise, those annoying grains all over the picture are caused by having an ISO that it too high, which cause a loss of detail. GOLDEN RULE: Before adjusting the ISO, try changing the shutter speed and aperture. Changing the ISO is your last resort.
Example of the light exposure that the ISO controls.
Example of the loss in detail-noise-that comes with higher ISO
Aperture
The aperture controls the depth of field. It can blur the background or foreground (etc) of a picture. It does this by focusing on one plane of the picture wherever you choose for it to be. A high aperture brings the whole photo into focus and clarity and having a low aperture only makes the subject you focus on clear whilst the rest is blurred. Higher aperture also means that less light will come into the picture so you will have to play with the shutter speed and ISO to get a good exposure. A low aperture does the opposite and makes the picture brighter,
Aperture controlling how focused the picture is.
Aperture controlling the depth of feild.
Shutter Speed
Finally, shutter speed. The shutter speed controls whether or not motion will be captured in the picture. It does this by adjusting the time it takes to close the shutters in the camera. A lower shutter speed allows more motion (and also more light) into the picture. On the other hand, if you have a moving subject and you want to capture it as if it was still and without showing its movement then you would use a higher shutter speed. This also prevents some light getting into the picture which darkens it and thus you would have to alter the other settings to get a better exposure in the picture.
Shutter speed controlling motion.
More Info On The Exposure Triangle:
Summary of the exposure triangle and what it does.