A page from the Google+ help center explains the purpose of the new Google navigation bar:
The Google+ bar, which appears at the top of Google products, is your connection to Google+. You can share what’s on your mind, view your Google+ notifications, access your profile, or jump to a variety of other Google products. For instance, to get to Google+, all you have to do is click +[your first name].
When you’re signed in and look at the Google+ bar, you’ll see your full name or email address displayed with a photo or avatar next to it. This helps you identify which account you’re currently signed in to. You can sign in to multiple accounts at once and switch between them using the Google+ bar.
One of the most interesting feature of the bar is notifications:
When you receive a notification, the notification area in the Google+ bar will turn red and show the number of new notifications. If you click the notification area in the Google+ bar, you’ll see a summary of your recent notifications. When you click a notification, a preview of the event that generated the notification will appear in the drop-down menu. You can take action on each notification right from the notifications menu, like commenting on a post or adding someone to a circle.
The navigation bar has been morphed into the Google+ bar and it should be more useful. Maybe at some point the bar will include notifications for Gmail, Calendar, Google Docs and other Google services.