The photoreceptor drum (or, in some photocopiers, belt) is the heart of the system. A drum is basically a metal roller covered by a layer of photoconductive material. This layer is made out of a semiconductor such as selenium, germanium or silicon. What makes elements like selenium so cool is that they can conduct electricity in some cases, but not in others. In the dark, the photoconductive layer on the drum acts as an insulator, resisting the flow of electrons from one atom to another. But when the layer is hit by light, the energy of the photons liberates electrons and allows current to pass through! These newly freed electrons are what neutralizes the positive charge coating the drum to form the latent image.
It's easy to imagine how you might project a copy of an image on a photoreceptive belt that has roughly the same dimensions as the sheet of paper containing the image. A problem emerges when you think about doing the same thing on a thin, cylindrical drum. How can the surface area of the drum possibly match the real estate on a sheet of paper? The solution is to simply rotate the drum while you're making a copy. If you rotate the drum in lockstep with the movement of the light beam across the original document, you can build the image strip by strip. After one strip of light is focused onto a corresponding swath of the drum, the drum rotates to expose a fresh area of the photoconductor. Meanwhile, the previously exposed region of the drum swings into contact with the toner, and then with the paper.
Because the length of a standard printed page is a lot larger than the circumference of the drum in a modern photocopier, one full rotation of the drum will only replicate a small piece of the page. The drum actually has to be cleaned, recharged with ions, exposed to photons, and sprinkled with toner multiple times in order to duplicate the entire original. To the casual observer, the process appears continuous, because it's all seamlessly coordinated inside the photocopier as the drum rotates.