The bounding box has has been there for both maya and mental ray. What is does is limits the region of space in which the displacement can occur. If you have ever tried to do a displacement and it does not displace as far as you expected it is usually due to the bounding box being to small. It's like a 3D clipping plane for displacement. It supposedly helps maya be more efficient using memory while computing the displacement, but why maya cannot make this computation on its own defies any logic.

The box is computed by looking at the shape node of an object that has a displacement attached to it, based on the color balance value.

So there is a definite order to setting up a mental ray displacement.

1. create the displacement map
2. create a material
3. apply the displacement map to the shader group node (I do it this way rather then connecting to the displacement input of the material because it works for both maya and mental ray materials.
4. set the max displacement for white / black using the alpha gain of the displacement textures color balance node. IMPORTANT - remember to check "alpha is luminance"
5. NOW goto the shape node of the object that has the displacements displacement node and click compute bounding box. You should do this every time you adjust the alpha gain as this determines the size of the required bounding box.
6. Set the render tessellation - for mental ray use a displacement approximation node or for organics a subd approximation node, for maya renderer you use the shapenodes displacement map tab and adjust the feature displacement (initial sample rate) and (extra sample rate) variables. Don't ask me how to logically pick the values though because like all things in mental ray it seems people just pull numbers randomly from their ass!

I have to keep a howto folder for maya with crib notes like this because every time I try to do displacement I cannot remember the right order to do things and where each thing that needs to be adjusted lives. This is why I keep complaining about mental ray being to convoluted!