The simplest definition of global illumination is "light transport between surfaces." In other words, it calculates the light that bounces off of one surface, and onto another, and another, and so on. A good example of this is an orange on a piece of white paper. Underneath the orange, the white paper will have a slight orange tint, since light is bouncing off of the orange, taking some color with it, then striking the paper, and bouncing again. In real life, we only see things because light reflects off of surfaces and eventually finds its way to our eyes. Traditional CG lighting does not use global illumination, and therefore does not calculate bounced light. Using traditional CG lighting, if you have a single light shining into a room, only the areas specifically hit by the light will be illuminated. Using global illumination, the light would enter the room, strike one wall, then bounce off, hit another wall, then bounce again, onward and onward, until the energy of the light is used up. This is the way light works in real life, and it results in an image which appears more realistic, since the room would be more or less filled with light, even if that light is very subtle. Sit in your room at night some time, and then just turn on a flash light. You will see that pretty much the whole room gets some light, even if it is just very, very slight. In traditional CG, only the exact spots being hit by that flash light would be illuminated. The rest would be completely dark. The benefit of global illumination is that it makes it easier to get realistic lighting, without having to set up tons of lights to fake bounced light. There are multiple ways of calculating indirect illumination, and achieve global illumination, but the two more popular methods are a subdivision mesh rendering method (commonly referred to as radiosity) and photon mapping. I won't go into the radiosity method, since Mental Ray uses the photon mapping method. There are two main benefits of photon mapping over subdivision mesh radiosity. The first is non-dependance on geometry. With subdivision mesh radiosity, such as is used in Lightscape and, I believe, Lightwave (as well as a bunch of other GI renderers), the more surfaces in your scene with the more boucned light, the higher poly-count the subdivision mesh needs to be, thus the more geometry is generated. Photon mapping works completely independantly of your poly count. The second benefit ogf photon mapping is that it supports all 3 forms of real-world global illumination (GI for short). Radiosity only calculates diffuse light reflection/transmission, whereas photon mapping calculates diffuse, specular, and glossy reflection/transmission. Photon maps are generated by having the light shoot small packets of light into your scene, named photons, which bounce around, taking color with them, until they run out of energy... much like real light works. This photon information is stored in a 3-dimensional image called a photon map. Similarly, caustics are a form of global illumination. Caustics, basically, is light focused by a refractive or reflective surface. The light patterns caused by holding a bottle of water up to a light, or the patterns of light at the bottom of a swimming pool, or the light reflected off of a mirror and shinging onto a wall are all caustics. Technically, as said above, caustics is a form of global illumination, since it is light indirectly illuminating a surface, but Mental Ray treats it separately for greater control. Again, a photon map method is used for caustics... then there's Final Gathering, which is a whole other can of worms. Final gathering (FG for short) is a process exclusive to mental ray, which is supposed to either A. help in global illumination or B. be used outside of global illumination to give "global illumination-like" effects. What FG does is create a hemisphere above each shaded point, and shoot rays within that hemisphere to "collect" indirect lighting. It only shoots one level of rays, however, so after the first bounce, no more indirect lighting is stored. This can help out GI because, by using FG in conjunction with GI, you can use less photons, and have FG "fill in" the areas missed by the photons. Overall, this results in a smoother rendering, without the noise typically associated with photons. So, overall the benefits to GI are: more realistic images and physical accuracy. The drawbacks are: SLOW RENDERINGS! There are tons of ways to speed up GI, caustics, and FG within Mental Ray, but typically speaking, a rendering using GI will be slower than a rendering not using it... personally, I feel that the quality gained outweighs the speed issue, though. Thats just a personal preference. Many people would prefer to add tons of lights to fake GI. Anyway, I hope this explination helps!
-Steve