Fuzz in this context is the background noise of random signals crossing the universe. You can hear it on radio and see it as those dots on TV. A fuzzy material .. fuzzy beard are all things indistinct, with blurred edges or indistinct shapes. So fuzzy as there's no discernible meaning to the signal seen.

Robert is correct. It relates to the days before 24 hour TV, and digital TV. If you have an analogue TV, and disconnect the antenna, or tune it off a station, you will see the fuzz.