Mozilla has clarified how to manage Firefox push notifications.
You need to give sites permission to receive push notifications, and now, if you have, you'll get a notification even if the site is not loaded in a browser tab. Users can manage the notifications by clicking on the green lock icon next to the address bar.
For developers..
To make this functionality possible, Mozilla helped establish the Web Push W3C standard that’s gaining momentum across the Web. How To Manage Firefox Website Push Notifications [blog.mozilla.org]
Here's more about Web Push notifications in Firefox 44 [
hacks.mozilla.org...]