When you add your events to your calendar from your mobile devices or Google website, you have the option to select which calendar it goes into. The 2 calendars from Google that we are sync'ing with MRSware are your personal one (usually just shows your gmail email address as the name) and your "Myname's MRSware Appointments" calendar.
When you add something on your phone/Google, if you put it in your "Myname's MRSware Appointment" calendar, the default is "Business". If you put it in your private Google calendar, it will default to "Private" in MRSware. You can adjust these defaults by going to the "Go To" -> "MRSware Sync" -> "Edit Subscription" menu in MRSware.
A Private Appointment can only be see by its creator, and anyone directly invited to it via the Attendees tab. A Business Appointment can be seen by anyone in the User's Management chain, as defined in the System Administration Roles and Filters.