Radiosity takes into consideration the interreflections
between diffuse surfaces. This affects all the objects with
radiosity set up in the scene. Not only is light coming from the light
sources, it also comes from all of the objects in the scene that have radiosity
set up and enabled.
All colors illuminate or reflect light back off of it, lighter colors more,
darker color less.
Radiosity is this light being illuminated from the object's color.
Some benefits from radiosity renders are more realistic scenes or images,
softer shadows.
A few example: If you have a shinny object that reflects objects around it,
with radiosity it
will also reflect the light source onto the objects around it. Or an object
that glows in the dark
the objects around it will receive light from the glow.

Cigarette without radiosity
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Cigarette with radiosity
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No radiosity
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Radiosity creates softer shadows
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40% radiosity no shadows
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Raytracing & radiosity no shadows
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Set up radiosity
To set up radiosity on an object go to the objects property window by right
clicking
on the object then select properties off the menu
or clicking on the green ball next to the objects name in the project window.