What is an Image Prior?
It is "prior information" on your set of images, that you can use in your image processing problems to enhance results, ease the choice of processing parameters, resolve indeterminacies, publish fancy papers no one ever use, etc.

For instance, you may know that the image, albeit noisy, should contain only 4 colors. Or that pixels follow a specific distributions. These priors, or their approximations, can be put into math form and can be merged into the processing (filtering, deconvolution, segmentation), and reduce the set of feasible solutions, generally through optimization algorithms.