The favorites tab as it is now shows a very basic description of your faved questions. You can sort them by recent activity and a blue notifier appears on the favorites tab if something happened.
So what you do, when you see the blue notifier, is order by recent activity and pick the top one(s).
However, comments and votes do not affect the latest activity date. I just got a notification on my favorites and none of the dates are today, so I have no way to tell what happened. I figure a comment was placed or a vote was cast. A comment might be important, so I'd have to check the comments on every single question and answer to verify that.
The activity tab shows all questions, answers, comments and edits of a person, as well as votes if they're your own. Reputation works similarly.
In my opinion, an overview like that of activity and reputation tabs would make much more sense for the favorites. I gather favorites are intended for keeping track of events, so a chronological list of events would seem to be the information you'd want. Perhaps with an indicator of where the new events begin.