Most of us can agree that in an ideal world students would be interested in learning just for the sake of gaining more knowledge. However, that’s not the case for all students across all subjects in school. Tools which provide extrinsic motivation work for a lot of students when there is little intrinsic motivation. (Check out this post for more on intrinsic motivation). It can get a student who otherwise wouldn’t be interested in a lesson to try to learn that lesson. It can also encourage better behavior in a student with problem behaviors such as a student who repeatedly talks out of turn or gets out of their seat without asking.
Again, ideally these students would behave out of their own personal belief that behaving well is what’s best for them and the class, but some kids need a little extra incentive. Extrinsic motivation can also been seen as a sort of stepping stone. A student who is otherwise not interested in a topic may start off learning it because of extrinsic motivation but may soon become interested in the topic itself, thus becoming intrinsically motivated to learn more.
Extrinsic motivation usually comes in the form of positive or negative reinforcement. Some positive reinforcement tools are stickers and other rewards, and good grades. Negative reinforcements include green/yellow/red charts where progressively disruptive behavior results in warnings or negative consequences, and calls home to parents.
Of course, several methods can be used simultaneously. For example, you can have a behavior chart up where students get warnings for bad behavior, a sticker chart where a certain number of stickers earned gets the student a prize, and a system where students get to customize their learning experience (for example by choosing which books to read) to ensure they’re intrinsically motivated to learn. You’re ultimately trying to appeal to each student.
In the end, which you make use of is based on your personal teaching philosophy and style, and what your students respond to.