Aperture and Shutter Priority modes are really semi-manual (or semi-automatic) modes. They give you some control over your settings but also ensure you have a well exposed image by the camera making some of the decisions on settings.
Aperture Priority Mode is often depicted by an ‘A’ or Av’.
In this mode the photographer sets the aperture, and the camera makes a decision about what shutter speed is appropriate in the conditions that you’re shooting in. When choosing an Aperture keep in mind that the camera will be choosing faster or longer shutter speeds and that there comes a point where shutter speeds get too long to continue to hand hold your camera (usually around 1/60).
Shutter Priority Mode is often depicted by a ‘Tv or S’.
In this mode the photographer chooses the shutter speed, and lets the camera make a decision about what aperture to select to give a well exposed shot. Most people switch to shutter priority mode when they want more control over how to photograph a moving subject.
Photo via Digital Photography School.