Facebook users now will be notified about any new notification with a small red dot on Facebook favicon (logo). The red dot would come in handy if you have muted your speakers for annoying notification sound. Whenever the user receives a new notification, a red dot will appear on the Facebook tab.
The red dot does not appear if you have the Facebook tab open and viewing it, but only appear if you are away from the tab. It will be same irrespective of receiving an activity notification, a message or a friend request.