The APT process is a photographic transfer system that can photographically transfer lines or solid blocks of colors onto acetate sheets (cels). A very similar process is used in silk screen printing. The process relies on UV-sensitive inks that cure when exposed to light and stick to the plastic sheet, while the ink in the non-exposed areas are chemically removed from the sheet. Its main advantage is that coloring - normally done via back painting after xerox scanning - can be controlled better and multiple versions made quickly. To put it simply: the drawings are photographed and the negatives then processed onto the cels instead of the typical photography. It also meant that a line on an animated character could be in color instead of just black (although xerography at this point could be done in colors too); this is known as self-colored lines.
This process was used on Disney's animated features such as The Black Cauldron, The Great Mouse Detective, Oliver & Company and The Little Mermaid.