When you take a long, long time to do something, you act slowly. And when things move at a low speed, they go slowly, like the storm clouds that slowly roll in during your school picnic.
A new driver tends to drive slowly, foot just barely pressing the gas pedal, just as someone learning a new language often speaks slowly, taking extra time to choose the right words. You may have also noticed that time seems to move slowly when you're doing something incredibly boring. In all of these cases, the adverb slowly describes something occurring at a low speed.