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Below are some examples.

 

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Standard beauty render – a couple objects on a plane and a mirror next to them

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Here the mirror object has been told not to reflect the sphere or accept its shadow. Here it's using the exclude option on the mirror set to redSphere.

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This is more subtle but you'll notice here that the green post now lacks the shadow cast from the sphere. The reflection also correctly omits this shadow. The green post was told to exclude the shadows subset of redSphere

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Here I tell the red ball not to reflect the green post. Perfect example of art direction, "Can you get rid of that green reflection?"

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This is a combination that shows you can be more flexible and creative. Inside the red sphere is a smaller blue diffuse ball. I've told the mirror not to reflect the red ball or its shadow. The blue ball is also told not to trace the red sphere (since it's inside, it would be totally black since the red ball would completely shadow it.) This lets you be creative in non-physical ways inside the render.

Caveat: Light sources may be blocked by hidden objects. Below we said not to reflect the red ball, and it doesn't but instead we get a black cutout against the dome light. To avoid this we set both the reflection and shadow sets to exclude the red ball on the mirror. This is because rays that don't reflect the ball are still blocked by the transmission/shadow rays.

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Without telling it to exclude the shadow subset, transmission rays block light sources. This is only an issue if seen against a light indirectly, in this case the dome light.