A risograph pushes ink through a mesh, like in screenprinting, but instead the screen is pulled over a cylinder drum, like a mimeograph. The technology is a combination of both techiques except automized, allowing for prints to be made for the fraction of the time and cost. How it differs from mimeograph and screenprinting is it's ability to print digital files (computer-generated imagery) directly from a computer.
In screenprinting, emulsion is used to block out the image. With a Risograph, it burns your image into a sheet of rice paper using a thermal plate. The burned image on rice paper is called a master copy. Think of the master copy as the stencil that you can keep reusing to make copies.
That rice paper is then laid over the drum, and each time you make a copy, the drum rolls as paper passes underneath. As the drum rolls, it pushes ink through the mesh, pressing the image onto the paper to make a copy, very similarily to the technology of mimeography.
There are two main processes in a Risograph: Master Making » Printing