What is the difference between the Aperture Priority (A) and Shutter Priority (S) modes?

In simple terms, here are the differences between the two modes:

• Aperture Priority (A) lets you choose the  aperture (aka f-stop) setting you want, but the camera chooses the shutter speed. 
• Shutter Priority (S) lets you choose the  shutter speed you want, but the camera chooses the aperture setting.

NOTE: You can choose the desired ISO in whichever mode you decide to use.

Combined with the ISO and the (aperture or shutter speed) setting you select, the camera decides the exposure for the image. Shutter speed, aperture and ISO all work together  to control the amount of light that enters the camera to produce the exposure.

In the A mode you have control of the lens aperture and can influence depth of field (DOF) . Just remember that the camera will choose a faster or slower shutter speed depending on your selected aperture. If the camera chooses a real slow shutter speed, you may need to use a tripod.

The S mode gives you the control to freeze or blur action depending on the shutter speed you select. Keep in mind that fast shutter speeds may cause the camera to choose a wide, open aperture, while slow shutter speeds may cause it to choose a smaller, more narrow aperture. Since the camera is choosing the aperture, just be aware that this can affect the DOF when shooting.