Sunspots are related to Aurora Borealis, in that both are manifestations of the 11 year solar cycle, which measures the energy output of the sun.
Sunspots, which are actually "cooler" areas on the sun's surface, compared with surrounding areas, are associated with microwave energy emitted by the sun, through a mechanism that is not well understood. This microwave energy affects the degree of ionization of the Earth's upper atmosphere (the ionosphere), which in turn affects medium- and high- frequency long-distance radio transmission. It does not affect satellite communications, except in extreme cases.
Also associated with the 11-year solar energy cycle are periodic emissions of plasma energy from the sun. The Aurora Borealis is a visual manifestation of the interaction between this plasma and the Earth's magnetic field.
(For purists only: There are some indications that the so-called 11-year solar cycle is really a 22-year cycle with 2 peaks.)