Aperture-priority describes a metering method which automatically sets (or displays) a shutter speed, based on the aperture chosen by the user. The term typically refers to a camera offering autoexposure—for example, one where an A or Auto position is found on the shutter-speed control. But aperture priority could also describe a method of manual exposure metering.
Aperture Priority may be be the preferred type of metering when control of depth-of-field is required. By specifying a small aperture, the photographer can ensure that objects at different distances are all in focus; whereas by specifying a wide aperture, the main subject of a photo can be isolated in sharp focus while the background is deliberately blurred. This is most useful in the context of fairly static subjects, where the exact shutter speed used is of less importance.
(Compare with Shutter priority.)