All groups are either public or private.
A public group is one that is listed in the Campus Groups Directory (the Browse Groups view of the Campus Groups portlet). This type of group has a public page that can be visited by non-members. It can have any of several membership options -- in some cases, users might be able to proactively join. In other cases, they might have to submit an application first, or they might have to wait to be invited by a leader.
A private group is one that is not listed in the Campus Groups Directory. A private group does not have any public pages that non-members can visit. The only way to join a private group is to be manually added by a leader for the group.