Extrinsic motivation is the carrot or the stick — when the motivation for doing something is an IF/THEN reward or punishment. We use extrinsic motivation all the time like paying people to come into work, or issuing speeding fines to make people slow down. It can work well for simple problems, basic compliance, and short-term results.
However, when you need long-term behaviour change, when creativity is needed, or you're tackling complex problems, external rewards and the threat of punishments can even decrease performance and productivity. Rewards only go so far if you want to inspire a hit album, create the next Oscar-winning film, or create a breakthrough product. That is, for most of the important work we do in our lives, including I believe parenting, using extrinsic motivators of rewards or punishments is likely to be far less effective than tapping into intrinsic motivation — motivation that comes from inside ourselves.
I like Dan Pink's Autonomy, Mastery and Purpose framework for intrinsic motivation. His TED talk on the Puzzle of Motivation is also a fun and interesting watch.