When it comes to insight, most people default to handling it intuitively (as opposed to deliberately), and to share it verbally whenever it occurs to them.
By managing insight we can more easily understand/align, share and improve the insight.
Let's say you have a hard time understanding something, or getting someone else to understand or get on the same page as you.
By writing it down you are challenged to ensure your own, proper understanding of the idea or concept, and can more easily have a discussion with someone else about where they agree or disagree.
So long as insight is located only within your own head, it can only be accessed by others when you are explicitly available to them, and by yourself as long as you remember it. By writing things down the insight can be made more easily accessible to anyone whom would benefit from it later, yourself included.
When insight is kept in the heads of individuals, the insight is fluid and, as a result, more difficult to improve upon. By taking it down we have a fixed and shared understanding of the insight, which means we can more easily elaborate and improve upon the insight as our understanding improves over time.
Read more about the specific advantages of practicing insight management within an organization.