The Google Calendar Integration pushes calendar events into any recipients who's email is associated with a Google Calendar Account:

The Google Account you tie this calendar to SHOULD NOT BE a calendar you intend to use to track events. This should be a "sacrificial" calendar that will often house multiple events for one "Job" in your calendar.
As example, if you have this event, with a school contact and three staff members, the Google Calendar you integrate here will have 4 events, one for each person associated with the job:

Each individual event in the "Integrated" calendar will manage the events in the calendars associated with each of the four people. So if you change the shift time for one of the staff people, that event in the "integrated" calendar will manage the event in that staff person's calendar.

The integrated calendar will also contain events for all of the options above:
Each of those can also be turned on and off with the check boxes above.