There are two sources of these thoughts: having read about, seen or heard something in relevant media; or something creative. For example, you may have heard a particular tune that you want to be able to play, or seen a particular playing technique that you want to be able to use; you may have seen a particular economics concept referenced in an economics publication. In terms of creativity, you might want to be able to play a tune that has sprung to mind as an idea; or you may have stumbled upon a novel way of looking at a concept.
Why are these interests important? They represent students' enthusiam for the subject and they can be creative output. When a student has come up with something they want to do, there is a sense of ownership that can be used to motivate the student to study. And any ideas are not something we want to loose or not see explored.
So what do we need? Teachers need tools to communicate to students the path to that knowledge they have expressed an interest (a learning roadmap) and the students/teachers need tool to enable logging of those thoughts, questions and ideas (to be explored, answered and implemented at a later date). And we need cultural acknowledgement and respect for these units of engagement, insight and enthusiasm.