Why Sunspots are a proxy for the sun's ultraviolet and X-ray output, which is what ionizes the F region. More sunspots means a denser F2 layer, a higher critical frequency and therefore a higher maximum usable frequency, so bands like 15, 12 and 10 meters open for long-haul work. At sunspot minimum the ionization drops and HF activity shifts down to 40, 30 and 20 meters.
Watch out A zero sunspot number does not shut down propagation or guarantee quiet conditions: the lower bands still work, and geomagnetic storms from coronal holes can disturb the ionosphere even with a blank sun. Sporadic E is a summer/E-layer phenomenon that is largely independent of the sunspot cycle.
More sunspots, more ionization, higher MUF. High sunspots = the high bands come alive.