what is the point of having the same object in multiple layers? What is the point of having the same object on multiple layers when the change you make on the object affects all layers selected? In other words, on what occasion can I use this feature effectively?
Camera:

If you have the camera in multiple layers, you can always see where it is positioned.

Lighting:

If you have lights in multiple layers, you can see all your objects under the same conditions.

Meshes:

If you have meshes in multiple layers, you might not have weird shadows caused by an object that isn't visible.

These are only a few; render layers are a very powerful tool and have many functionalities.