Private calendars are only viewed by the member that posted it so it is just as it says a private calendar.
Public calendars can be set for each group
Control Panel » Group Management
Select » Site Permissions to the right of the group
Then change the "Can create new calendar events" to 1
This also allows the user in that group to add a topic to the calender while posting.
Currently your site does not allow the user group to add public calendar events. If that is the group I am in.
