The "planes of the head" are the simplification of the constant curving of the head into areas that share a similar orientation. Meaning, take the curved surfaces of the head and flatten those surfaces to get the fewest flat areas while preserving the basic volume of the head. Think of the forehead, it is basically one big area that faces in a certain direction. The tops of the cheeks another area that generally faces in one direction, the temples another. Identify and outline these areas to get your "planes of the head".
Loomis is suggesting that there is a formulaic approach you can take to do this that results in the same general set of flat areas that to together make up a angular, flat paneled version of a human head. Then you have simplified shapes that will be easier to put into perspective and serve as the under-drawing for a smoother final version.
You need to be able to draw an arbitrary flat plane shape (a polygon) from different perspectives. If you can draw a given triangle or trapezoid from different points of view then to draw a head you would use the same technique with the collection of arbitrary flat plane shapes that you have extracted from the head and memorized according to Loomis.