This panel of the Object Properties dialog supports mental ray rendering; specifically, the indirect illumination features caustics and global illumination. They control whether objects generate or receive caustics or global illumination.
These settings are ignored where they aren't appropriate. For example, lights can be set to generate caustics, but for a light, the Receive Caustics setting has no effect, as lights aren't renderable. Similarly, these settings have no meaning for cameras.
Also available on this panel are controls for setting displacement parameters on a per-object basis.

These settings let you specify how an object interacts with the final gather process.
These settings determine whether and how the object participates in the simulation of caustics and global illumination (photons). To use these capabilities, the respective checkboxes must also be enabled on the Render Setup dialog's Caustics And Global Illumination rollout.
Generate Caustics When on, the object can generate caustics. When off, the object does not generate caustics. Default=off.
Receive Caustics When on, the object can receive caustics. That is, caustic effects are cast onto this object. When off, the object does not receive caustics. Default=on.
Generate Global Illumination When on, the object can generate global illumination. When off, the object does not generate global illumination. Default=off.
Receive Global Illumination When on, the object can receive global illumination. That is, reflected light is cast onto this object. When off, the object does not receive global illumination. Default=on.
Displacement groupThese settings let you apply displacement parameters on a per-object basis.
Both the mental ray renderer and the iray renderer use these displacement settings.
Renderer panel
Shadows and Displacement rollout. Turn off to make settings on a per-object basis. Default=on. Large values of Max. Displace can affect rendering performance. On the other hand, if this value is too low and the renderer returns greater displacement values, the Render Message window displays warning messages to that effect. You can use these warnings to fine-tune the value of Max. Displace.
When using only height maps in the scene, make sure this option is off. If some objects in the scene use height maps while others use standard displacement, apply smoothing on a per-object basis.
When on, the renderer simply smooths the geometry using the interpolated normals, making the geometry look better. This result, however, cannot be used for height map displacement because smoothing affects geometry in a way that is incompatible with height mapping.
Max Level For example, using the default value means that the renderer can subdivide each displaced mesh triangle into as many as 4,096 smaller triangles.
Parametric Regularly subdivides each triangle of the surface. This is the fastest and the best option for scenes that are regular and mostly flat. There is an upper limit of 8 million triangles per object.