heres a pretty good explanation, I copied it from a page over at
www.gamedev.net and its written by a guy named Nathan Vegdahl so props goes to him.
'Radiosity is an addition to typical 3d rendering methods that increases the realism of any given image by a multitude. The theory behind it is that light does not just bounce off of objects and go into a persons eye, it also bounces off of objects onto other objects and then into the persons eye. And it also bounces off of objects onto objects onto yet more objects and then into the persons eye. And you can trace that until certain rays of light have bounced off of every single object in the room before it even reaches the eye. And that is actually what happens in real life! It results in something that one might reffere to as "color bleeding".
For an example of this, you could take a tennis ball, and hold it about a half inch away from a piece of white paper. If you look closely, the part of the paper that the ball is closest to has become a slight tint of yellow. That is the phenomena of radiosity at work. '
Hope this makes it a little clearer for you
//Matt