Radiosity is a term used in graphics - it is the name for a series of calculations which emulate the reflection of light. This may seem a bit weird but think about this: light reflects off objects, even matte objects (i.e. non-reflective objects). Light also changes color when it is reflected which gives off a colored "ambience".
Practically, you shove a lawn chair on to a patch of grass. Assuming that the grass is green and the chair is white, the bottom of the chair will turn a greenish-white color. The scientific explanation to this is that sunlight hits the grass and then the green spectrum of the rays bounce off onto the chair - so the chair is being lighted by sunlight and the green radiosity of the grass.
Light received directly from a light source is called "direct light". Light bounced from an object is called "indirect light".
Now, if you have a 3D program at hand, think about this. Make a room with a few things in it and then put one light somewhere, such as in a desk-lamp. Render it and everything will be black except for a little patch of light coming from the lamp.
Then, go into a room with all the lights off, windows shut and doors closed (bring a torch or a military grade light-amp unless you have natural night-vision). It's pitch black. Turn on the desk-lamp. It's not pitch black anymore! Sure, the patch of direct light stands out and is visible but the room is glowing with an ambiance. Now, get a colored surface - such as a red folder or a piece of plastic. The ambience is gray - the desk-lamp is shining onto your white desk. Put the folder down under the light. The ambience turns red! The indirectly-lit surfaces will have a reddish tint.
Now you should realise the importance of radiosity.
I actually went as far as making a room in POV-RAY, putting 4 lights into it (in little domes so that the light is cast at the ceiling) and putting a few other objects in. I rendered it without radiosity and all I saw were 2 patches of light (from a camera angle that looked at a corner of the room).
When I rendered it with radiosity it took longer and had strange image artifacts but the ambience lit up the whole room and the change was obvious. Eventually, after turning up the quality I got longer rendering times, less artifacts and more subtle lighting.
If you want to see the rendering, go to the RenderZONE from my homepage and pay careful attention to the picture titled "My Room". (And "ooh-and-aah" at the other images if you have time [grin])
http://connexus.apana.org.au/~mikuto/darkyEmil Mikulic, 8th July 1997.