To add to Neil's response, a copy stand allows you to keep the camera film/sensor plane parallel to the subject (assuming its not a book) to keep keystoning distortion from creeping in.
Some tripods that do allow for a center column to be mounted horizontally can be used in the same way, but a dedicated copy stand has provisions for lights typically at 45 degrees to the subject allowing for even lighting, with a tripod, you'll another piece of equipment for even lighting.
Some lenses, like the old 60mm Micro are great flat field lenses with minimal distortion. Used to be said that it was a great copy stand lens because of the lack of distortion, close focusing and angle of view, wide enough to get a good subject in, but not too long that the camera couldn't get far enough away to fill the frame with a larger subject. I think the 40mm Micro does the same for DX bodies.