While going by many different names ("Bridges over many things", "new bridges", "magic bridges"), the functionality of this new feature is quite simple; it lessens the restrictions of what can live underneath bridges. Previously, only straight, unsignaled track/road/canals that was perpendicular to the bridge could be built beneath a bridge. As you can see from the picture below, many of these limitations have been removed.

The New Bridges feature in action (shown also with the High Bridges patch enabled)