There isn't much to help on since that is true. The backlight is always on, regardless of the color. Black requires voltage to the liquid crystal display to become opaque. White means it is "off" (transparent), which requires no energy.
It is easy to get confused if you forget that the backlight is always on. I wouldn't say that it takes less energy to run a black CRT compared to a LCD because of the electronics that have to be energized in the CRT.