Intrinsic motivation is motivation that comes from within. It comes from the personal enjoyment and educational achievement that we derive from doing that particular thing. For example for people who love music, their motivation to practice the instrument, attend classes etc is intrinsic motivation.
Extrinsic motivation is motivation that comes from things or factors that are outside the individual. For example being motivated to work hard at the office because you are looking for a promotion is a type of extrinsic motivation. Social recognition, money, fame, competition or material achievements are all examples of extrinsic motivation.
Extrinsic motivation can be further categorized into moving towards motivation and moving away motivation.
Moving toward motivation is, as the name suggests, motivation from desiring to move toward, obtain or achieve something. When you give out rewards or incentives for doing something, it is using moving toward motivation. Motivation to pursue money or to achieve something is a form moving toward motivation. The main focus of the moving toward motivation type is to gain pleasure.
Moving away motivation is the opposite of moving toward motivation. The reason it is able to motivate is not because of the possibility of getting something, but rather due to the prospect of avoiding something.
For example, for some kids their motivation for brushing their teeth properly is primarily from the desire to avoid going to the dentist rather than to have healthy well maintained teeth. So their motivation stems from wanting to move away from something rather than to move toward it.
The main focus of the moving away motivation type is to avoid pain and fear.