Collotype is a complex printing technique originated in Germany. Due to the extreme precision required to be made, it has been substituted by offset printing.
The last collotype printers in the Western world have shut down in recent years. Japan is the last country where this technique is still used for commercial products.
Simply put, the process implies 1) the application of a specific type of gelatin to a board, which will then be left to dry at a controlled temperature; 2) the carving of the shapes to print onto the dried gelatin, which will now be similar to a plastic board; 3) the application of collotype-specific ink to the carved board.
The colored board will then be processed in a machine which will fix the color onto paper through the use of ultraviolet.
The process is repeated several times depending on the colors required. Since each color tone is applied separately, even different tones of the same color will require different boards.
The process is clearly explained in this video, provided by Benridō, in Japanese with English subtitles.