It contrasts with intrinsic motivation, which is an internal force such as interest in learning a language to communicate with other people or for further personal development in general.
Example
Exams preparation classes often have a high degree of extrinsic motivation as learners are attending class to pass an exam, often for work purposes.
In the classroom
Many teachers believe that intrinsic motivation is rare in learners. Learners often have a mixture of the two types of motivation, or change from one to another.
Further links:
https://www.teachingenglish.org.uk/article/motivating-teenagers
https://www.teachingenglish.org.uk/blogs/rachael-roberts/rachael-roberts-motivation
https://www.teachingenglish.org.uk/article/motivating-unmotivated