The wiki page on Hopf Fibrations has a brief application section - but its still a bit too technical. Any sophisticated HN readers have a more simplistic explanation of the applications of these structures?

I've done some light investigation myself, but math is a minor hobby for me, not a specialty. I really like the demonstrations in the post - allowing parameter adjustments and some clearer technical explanations gives you an intuitive sense for how the Hopf Fibrations "move".