Extrinsic means not connected to the essential nature of something. New cleats are extrinsic to making the soccer team. How you play is what gets you on the team, whether your cleats are old or new.
If the ex in extrinsic makes you think of external or extra you’re on the right track––all these ex words are talking about something that is outside, or above and beyond. You often hear extrinsic paired with its opposite, intrinsic, which means part of something or someone's essential nature. If being sweet-tempered is intrinsic to your personality, you might not even know how to get mad.