It almost certainly uses an image analysis technique called "deconvolution." Reading the wikipedia page on it is a good start but it is awfully technical and you might be left just knowing the name of the technique.
I did read a blog somewhere where is suggested that the inverse transform that is needed for proper deconvolution can be known since the blur that comes in our digital pictures comes from the needed anti-aliasing filters in the camera's hardware. This seems like a good theory to me. Except that that would only work for images that were focused properly, not blurry as a result of any hardware limitations. Topaz's infocus certainly works with improperly focused images, at least it does according to their website!