Nothing. The enrolled column refers to those students who have registered for the class. The visible column lets the class staff know whether or not a student's name is viewable by others in the class. As long as a person's name and e-mail address appears in the membership list, they are allowed to login to the class site.
A note regarding visibility: The students can decide whether or not to make themselves visible to the entire class. The instructor cannot do this on behalf of the students. Students can do this by clicking on edit in the visible column of their row.
If this article does not resolve the issue, please use the [Stellar Recon page].