The window shows the value of the cosine for each of the angles between the selected normal (left, right or both) and the direction relative to a light. In the case of an omni light, the direction is from the vertex to the light. For a directional light, it is the reverse of the light's direction and, in particular, the xyz coordinates used in defining the light. Also, when the two vectors are normalized, the cosine of the angle between them can be computed as the dot product of the two vectors.
Note that when the dot product of two vectors is negative, the angle between them is greater than 90 degrees in which case we set the value to zero. Now observe that as the dot product (cosine) varies from 1.0 to 0.0, the illumination provided by the light diminishes. For example, initially the cosine of the angle between the left varying normal and the right omni light is 0. This means that the left face at the common edge has zero illumnination from the right omni light. On the other hand, the cosine of the angle relative to the right directional light is non-zero and, therefore, there is a bit of green color reflected by the left face at the common edge. You can validate this by disabling the right directional light.