When you propound an idea, you put it forward. If you tell your teacher that listening to music in class would help students do their work, then you propound the idea that music can be a motivator.
The word propound is a little bit formal and often used in reference to something that’s weighty and serious. Beloved by academics of all types, you might hear someone propound, say, his theory of logocentrism in the works of Jacques Derrida. Don’t worry: you don’t need to understand the theory, you just need to understand that propound means he’s putting it out there.