This means that the musician was doing well and was having their songs listened to and on the charts. It means their songs are popular. When personal problems occur, their songs may be less listened to, therfore making their songs less popular and off the charts. They may not do well because of the problems. When they make a major comeback, it means that their songs are once again popular and in one of the top spots. "Charts" mean the most popular songs of that week.