Disclaimer: This may be slighlty wrong, but it will give you som idea.

The mental ray renderer, gives you the ability to use FinalGather, GlobalIllumination, Caustics and ordinary raytrace renderings.

FG (final gather) is a way to calculate the light in a scene, where every surface becomes a source of light, as the light is reflected and bounces off surfaces everywhere.

Gl is a way to send out a given amount of photons which light up the surface, wherever the photon hits it. Using GI alone may produce some artifacts as the number of photons may be insufficient to get into all those corners and such.

FG and GI can be combined. I have yet to try this.

Caustics, well I don't know much about it, but I guess it is a way to calculate how light passes through materials such as glass for instance, and then how it scatters onto other surfaces beyond the glass.

I cannot tell if mental ray is any better or worse than the next renderer, neither in quality or speed.