Cycling is when you have two exact molds of the same disc where one of them is more beaten in than the other. Many advanced or pro players either:
Don't like to play with a beat-in disc Only play with a disc that's slightly beaten-in.
That's when they start to cycle discs. In the case of a player who doesn't like to play with a beat-in disc, they'll try to use their new disc only when necessary and use the old one during warm-ups or practice games. This helps increase the longevity of their new disc.