According to the Science behind both renderers, unbiased really means that the renderer will just keep on going until it converges to a correct solution, but biased renderers are still quite accurate at insane settings... both type of renderers would look identical to the human eye! It's just biased renderers allow limits to the behavior of rays in order to reduce rendering times.
unbiased:
eg. a car curves to the left and keeps curving left until it forms a circle.
biased
eg. a car curves to the left, but the driver in the car decides to stop just before forming a complete circle becuase he has covered enough distance to see that it is a circle.
in a biased render: imagine stopping maxwell after a few samples, then interpolate the grain until it becomes smooth, you wil notice blotchiness appears along the walls such as in a interior rendering of a square room.