This saying is a good reminder to get group support. If you are trying to stay sober on your own, it's no fun and probably hopeless. Eventually, you will be in a situation which will cause you to relapse. When you are at an AA meeting, you are with people who are successfully dealing with the same disease that you are. Meetings give you an immediate sense of camaraderie. Even if you feel like you have philosophical differences with the 12 steps, trying them might be easier if you are getting help from someone else. It's like walking through the snow is easier when you are doing it with your dog that you love. Furthermore, sometimes in early recovery especially, we don't like ourselves very much. So trying to stay sober by ourselves isn't a lot of fun.
Find a meeting where you like a few people and introduce yourself to them.