I see these Matte boxes, what exactly do they do?

The primary job of a matte box is to eliminate off axis glare (sun/lighting/reflectors) from hitting the lens at too shallow of an angle. This helps prevent the image washing out as the light illuminates the sides of all the microscopic particles that collect on/make up the surface of your lens. It also helps to eliminate the lens flares that can occur if you have a light source just out of frame. The more expensive ones will allow you to drop filters in it between the box and the lens.

The reason they are called Matte boxes, however, is because they were originally intended for making use of mattes, which is primarily done digitally now (think blue or green screen).

Here's a decent description of matte painting:
http://library.thinkquest.org/10015/data/info/reference/techniques/matte.painting.html

The matte box holds these painted mattes (pieces of glass) and blocks out light from the sides to ensure a quality matte.