Aperture Priority (abbreviated A or Av) is a camera mode common these days on most cameras. This setting allows the user to select a static aperture and the camera automatically selects the shutter speed to achieve the proper exposure.
The primary purpose of this setting is to control the depth of field or achieve good bokeh. This is very useful in HDR, portraiture, special effects, and landscape photography.
Also see: Aperture, Shutter Speed, HDR, Bokeh and Depth of Field.