In my opinion, a minor doesn't really help your application for med school except at interviews, where you may be asked about it. Then discussing why you chose that minor could set you apart from the other applicants. Also, a minor could help "weave" the story of your application together further. For example, if you have a bunch of leadership positions and talk about the physician's role as a leader in the workplace/healthcare and take management as a minor, you can essentially talk about how your minor has developed your leadership skills, thus making you a more suitable candidate for medical school.