Toolbar Notifications allow you to view and moderate comments right from the toolbar, anywhere on your site or across WordPress.com.
To use notifications, a user of your site must go to the Jetpack admin page and link their account to a WordPress.com account. That ensures that they have their own channel for notifications. This step isn’t necessary if you’re the main user who connected the Jetpack site to WordPress.com, that serves as the channel for your user.
Once you’re connected (main user) or linked (other users) from the Jetpack admin page, click on the notifications icon in the toolbar and log into WordPress.com if you’re not already. Now you’re set to view and moderate comments on your site and from anywhere on WordPress.com. Note that in order to moderate comments from the notifications toolbar menu, a user must have comment moderation privileges (if the user can moderate comments elsewhere, they will be able to in notifications also).
For more details on using Notifications (and keyboard shortcuts) see the WordPress.com support page.

Does this work across multiple installs of JetPack? Eg the notification bar on site-A will display comments from site-B, in addition to WordPress.com sites?
Yes, if you have an account on site A and site B, and both are linked to your WordPress.com account, it works as you described.
Martin, that could get extremely confusing unless it is going to identify on which site the comment was posted, as well as the post on which it was posted. Especially for those of us who have been around WordPress for a while and may have dozens of single and multi sites that all use a single wordpress.com API key, and have years of posts that could kick up as commented on.
Could you add to the wish list, a visual indicator of the site and original post date, not just a hyperlink to the post?
Many thanks.
Good idea, thanks for the suggestion.