Besides the other good answers given, I want to add the fact that some physics commonly is not driven by the server or even know about by the server and is a common trick to make the world seem more rich without adding overhead to the networking or server side processing.
For instance there might be debris you can kick around on the ground or blowing around in the wind that interacts with other objects, or maybe you can push dead bodies around.
If the physics is purely decorational, and doesn't affect movement or gameplay in any way, you can have it happen on the client side completely.
Different players will see things differently (like, if you shoot a can on the ground and it flies away, other players may not see that can fly away) but there are a lot of cases where that doesn't matter that the experience isn't the same for all players, and having client side physics simulations can really improve the look and feel of the online game.