LuxRender is a new, open-source, free software rendering system for physically correct, unbiased image synthesis. Rendering with LuxRender means simulating the flow of light according to physical equations. This produces realistic, photographic-quality images. – LuxRender.net
As I understand it, an unbiased renderer is one which attempts to simulate the physical properties of light. Biased renderers allow you to create images which would not be possible in the real world. For instance light in a biased renderer travels directly from light sources to objects in their path. Once the light strikes an object it stops there. Any surfaces in the shadows would be perfectly black. In unbiased* renderers the light travels from light sources to the objects in the scene and then continues to bounce around until then energy drops to an insignificant level.
* July 4, 2009, When I originally posted this I wrote biased which is incorrect. Unbiased = close to real world physical light simulation. Biased = fake, less realistic