calendar
On OS X 10.9.5, the Calendar.app toolbar sometimes adds this button:
There's no tooltip, and the Calendar toolbar isn't editable so there's no way to show a label for it. I can't find anything in the online documentation about it.
I think it has something to do with remote/subscribed calendars, but what, exactly?
So, it looks like Outlook for Mac 2011 is incapable of proposing updates for meetings sent by other people (or, for meetings sent by Outlook for Windows users), regardless of standard permissions.
Looks like this is another missing feature alongside voting buttons and easy calendar sharing requests. In Outlook for Windows you can propose updates that the organiser can accept or reject; in Outlook for Mac there seems to be nothing like this.
This is based on the fact there are 'Send update' options seemingly only for meetings that you are the organiser of:
It looks like the only possibility is to decline the meeting, then send your own - or, if that's not an option (which will be true any time it's not appropriate to just become the new meeting organiser), you need to email the organiser (e.g. in a 'Decline' comment) and ask them to do it for you.
A bit rubbish because, if they're a Windows user, they'll think you're a fool who can't find the 'Propose new time' button, and they'll think you're wasting their time asking them to do simple tasks for you...
Uncheck the calendar in system preferences -> Accounts (or delete the whole account, I don't think it makes a difference).
Then delete files associated with the Calendar ~/Library/Calendars ~/Library/Caches ~/Library/SavedApplicationState/com.apple.iCal.savedState
Reboot Open calendar, check if it opens normally. If it does, quit calendar, add the account (or tick for calendar syncing) again, and reopen calendar.
Perhaps use something like Remote Desktop, VNC or TeamViewer if you don't have physical access to the computer.
Best Answer
This is the Notifications button.
Source: Calendar: Reply to an event or calendar invitation
The notification button also shows when changes are made to a subscribed calendar. In this case, the standard Accept/Decline/Maybe buttons are replaced by a single OK option to dismiss.