Notification badges have not change a lot during the last couple years. They were always simple counters that showed the number of unread notifications from a specific app. This is now changing with Nova Launcher introducing a new, innovative feature.
This new feature is currently only available in the latest beta update of Nova Launcher and might not work 100% of the time due to its early development stage. Dynamic notification badges replace the classic counter with new icon badges which show more info about what notification the badge refers to. For example, when you have an unread message the badge displays the contact picture of the sender. Since this service extracts icons directly from app notifications, there is no need for additional support for this feature.
In the official Google+ post, the Nova Launcher developer states that these dynamic badges are much better and more useful than the classic counter thanks to their higher reliability and being more useful to the user. This seems quite accurate since the dynamic badges do deliver more info than the classic ones.