Definition: Spinning the pedals on your bike is a pedaling techinque where you pedal fast in an easier gear. With higher RPMs of the pedals, you can go just as quickly as when you're a masher, but with less fatigue in the long run. Many experienced cyclists believe that spinning is best for long climbs, as opposed to mashing the pedals.
Conceptually, I'm sure you can see how this phrase is related to its usage in describing "spinning", the exercise people do when they take spin classes.
Examples:
"If you're spinning the pedals when you climb, you'll be a lot better off than if you were mashing your way up all those hills."
