First, note that registered student organizations must be accessible to all
students, so their group sites must be public. For other kinds of groups:
You would choose to make your group private if you need to restrict membership
to specific people, for example, the members of a committee. Keep in mind, however,
that making your group private means that you will need to specifically admit
or deny each person who requests membership in your group through the "Manage
Members" area of the group portal. If your group does not really need to
be private and/or you don't want to have to manage the members, then make your
group public.