Before we startThis topic has been, and still is, mostly about marketing and buzzwords. It has little to no relevance in a 3D artists daily life. However, it pops up in forums and discussions from time to time so I want to address it briefly.
In computer graphics, unbiased rendering refers to a rendering technique that does not introduce any systematic error, or bias, into the radiance approximation. Because of this, it is often used to generate the reference image to which other rendering techniques are compared. Mathematically speaking, the expected value of the unbiased estimator will always be the population mean, for any number of observations. Error found in an unbiased rendering will be due to variance, which manifests itself as high-frequency noise in the resultant image.
Well... that wasn't particularly helpful, was it?
A more useful explanation (but less scientifically appealing) would be to say that
unbiased rendering means you don't cut corners. Optimizations to the rendering process, like adaptive sampling, need to be seen as a bias.
The problem now is that this more or less disqualifies every single renderer out there as a truly unbiased renderer. Why? Because a renderer that is truly unbiased is useless due to its abysmal speed. This obviously wouldn't be a good marketing strategy so calling a render unbiased is drawing a somewhat arbitrary line somewhere. This also means that the term has lost its original meaning and is subject to personal preference.
The takeaway here is that it is more useful to understand render technologies and judge renderers by their features than choosing a renderer by its marketing jargon. If you want to know more and what is usually considered to be an unbiased renderer in the real world, look at the link below. Highly recommended.