Question: This would be an excellent figure for someone to try and explain. Understanding what this figure is visualizing is the first step in understanding many of the integrals in this lecture. Another question is: why is the figure on the right look like a flipped version of the figure on the left?
Each point in the circle is a direction. The brightness at that point is the radiance in that direction.
The reason that the picture on the right is a flipped version of the picture on the left is that for ideal specular reflection, the direction of the ray gets flipped. So if Z is the normal, a bright ray coming in from the -x, +y direction (relative to the camera) is seen on the bottom left of the left image. It will leave in the +x, -y direction, so it corresponds to a bright spot in the top right of the right image.