As you can see now, each of the boxes has a different material assigned
in their VRayOverride
Reflect material. The first one has a red diffuse color, the second
ones have green and the third one has blue. VRay uses those materials, when
the objects are seen in reflections. In our scene the environment is
actually a reflective surface, so the boxes are being reflected. On the
other hand you can also notice that the base material of the boxes is also
reflective (Fresnel type) and the middle ones are seen with their
VRayOverride Reflect
material in the right box.

The next render comes even more complex as the
VRayOverride Refract material of the
boxes is activated as well. From left to right follow: a cyan diffuse color,
purple and yellow ones. Those materials are set so, that when seen through
refraction, VRay will consider and render the objects with them. As you can
see the Reflect materials are still affecting
the render image. If you take a closer look at the lens' edges you will
notice the green reflection, which is actually the that reflect material of
the middle boxes. While VRay had been tracing the rays on the lens'
surfaces, those polygons on the edges had first captured a reflection, so
that's why there are green traces.

This example shows how the use of a GI material will affect the
rendering.
Scene rendered with 2 VRay materials

Scene rendered with 1 Base + 1 GI Mtl

As you can see the scene represents a square-type room. There are window
openings in one of the wall. There is a Direct Light coming through, which
simulates the Sun. The Floor has a texture in the Diffuse map slot. All the
rest - the walls, the ceiling and the teapots have a Default
VRayMtl with a Diffuse
Color (200,200,200).
On the first render, it is absolutely visible that all the walls, the
ceiling and the teapots have been rendered in some light brown (pale
pumpkin) Color, although they have a light-gray material assigned. This is
because of the Color Bleeding, which is generated by the
GI calculation.
On the second picture, the scene is rendered with a
VRayOverride GI material assigned to
the Floor.
This material contains in itself the initial 2 Vray materials - the
Floor's and the Walls' ones. So now assigned on the Floor object, VRay will
know that while calculating the GI it has to
use the GI material /in our case: Walls
- VRayMtl with Diffuse Color(200,200,200)/
and during rendering it will use the Base
material /in our case: FLOOR - VrayMtl
with texture in the Diffuse Slot/. Result of that is quite different from
the previous render as the Color Bleeding has gone. Of course this depends
entirely on our choise for the GI material.
For instance if we had chosen a bluish colored material, the final result
would also be tinted slightly to blue, like in the first render - with the
pale brown colors.
In this simple scene the result of the second render can be produced,
with a pre-saved irradiance map, calculated with just the Walls' material
assigned to all the geometry.
But for a much more complex scene, with lots of different geometry,
shaders, textures etc., using the VRayOverride
material can be very helpful.