Perspective control is a feature on some lenses for 35mm and medium format cameras that allows the photographer to correct certain problems of image distortion, like parallel lines of a tall building coming towards each other. In a view camera, the photographer can shift the position of film relative to the lens of the camera, thus elliminating this distortion. In a 35mm or medium format camera, the camera is a solid unit and cannot be shifted in these ways, thus the creation of the perspective control lens.
A perspective control lens can be shifted to correct distortion or fix other problems. It does this by having a larger circle of coverage than normal lens, so that when the lens is pivoted or shifted, it still provides an image that covers the whole frame. Perspective control lenses are generally expensive because of the cost of physically larger optics and because of limited demand.