In Calendar, what does "turn of shared calendar messages in notification center" mean?
Yes, that makes them shared. 

My wife and I have a few iCloud calendars that we share. With this option not checked (as it is in your screen shot), if she made an adjustment to one of them on her iOS device or Mac, I would have a new notification on my iMac notifying me of the change. 

Similar to this screen shot, but instead of saying 'Coffee in 24 minutes', it said '[other persons name] changed [event name]' or something similar. 



If you check that box, these notifications would be suppressed. This feature was annoying me (because of another bug, many of our events had alerts put on them that we didn't want, so I checked this box so we didn't go crazy trying to fix them). Something similar may show up in iOS 6 as well.

Finally, I have only used iCloud calendars with this, so I am unsure if it works exactly the same when using a shared Google calendar. I would assume it would since its still going to the same store, but have no way to test.