What are Grey Balls used for?
Yes, they are used for adding visual effects in post. The mirrored ball is for creating an environment map or reflection map. These maps provide the same lighting from the real scene to the virtual scene where graphics are created to composite into the existing scene.

I believe the grey ball is used for recording more diffuse lighting from all angles, though I'm not positive.

The cards with either black and white or colored square patterns on them are for motion tracking, image stabilization, and orientation. They're often used to replace computer or mobile phone screens, for example.