A variant strain of science fiction where lovable technophile monks are the heroes of misadventures unfolding in a post-apocalyptic era. These wacky abbots and friars play crucial roles in preserving scientific and philosophical knowledge, even though it gets warped and twisted through the filter of religious superstition, often to ridiculous extremes. Bonus points for radioactive mutants, deformities, plague, witch burnings, alien visitations, nuclear fallout. Like other -punk genres, this one has nothing to do with punk rock, except maybe if you count the mutants.
Contrast with cyberpunk and steampunk, two related sci-fi "punk" sub-genres.
Walter Miller's A Canticle for Leibowitz and Neal Stephenson's Anathem are the twin towers of Monk Punk, a sci-fi genre which might as well include The Name of the Rose, since Europe's Dark Ages were pretty much a post-apocalyptic nightmare of their own.