Obviously you will receive a range of different answers to this question. For me, when I read this book what came out of it was the way in which we can find solace and peace through music. The description of the music that is played by Bud's father's band is truly beautiful and shows the role of jazz during a very difficult time for many Americans in helping them to transcend their difficulties.
Since you ask what we learn from the book, it sounds to me like you are looking for a theme. A theme is the lesson or moral you learn from the book, or the point the author is trying to make. In this case, I think the importance of belonging is a good theme.
Here, I have included a link to the enotes theme page: