The thing about film, as opposed to video, is that the detail captured by film can theoretically be precisely mapped to the very center of the dye clouds that make up the grain, whereas there is no way to know which pixels of a video image contain useful detail. Here’s a quick and dirty visualization of the idea:
Say that this is the edge of an object. When captured on film, photons of light bounce onto the film and react with microscopic silver halide crystals. When the film is developed, the halide crystals react with the surrounding substrate and create dye clouds, which can be viewed as grain:
Now this sharp edge is blurred by the process of creating the dye clouds. Compounded by several layers of colored substrate, the grain becomes complicated, such as in the ‘before’ example posted by Poita above. In that example, beautiful though it is, the image can never be sharper than the sharpness of the dye clouds. To understand this, consider that no matter how many pictures are taken of a sharp edge, each one will be blurred by the radius of the dye cloud. No matter how these are averaged together, and no matter at what resolution, this dye cloud radius remains.
Now if you were to map the centers of the dye clouds, it may look something like this:
At this point the algorithm can determine the most valuable parts of the image. The key to greater resolution is that each frame of film contains a slightly different grain pattern, meaning that the centers of these dye clouds shift. Out of 20 or so frames, they may all have a substantial number of dye cloud centers that are in unique positions. Finally one can intelligently find the points in the film most likely to contain unique image data, on a photon by photon basis. This is not possible with a digital video signal, since again, there is no way to tell which pixel is more likely than another to contain detail rather than noise. Combining enough images makes it possible to recover a clean image with a sharp edge, almost regardless of the coarseness of the grain.
With an averaging super-resolution algorithm blurriness can never fully be removed. with Halide Crystal mapping you can potentially regain the unblurred edge.