Reilly rhythms are so-called rhythm lines in the face. They help you position features correctly and typically map to underlying bone structure of the skull.
You are free to deviate from the rhythm lines other people use. The idea is to find lines things are aligned against.
The way to use these Reilly rhythms: first practice the above a few times until you memorized them somewhat.
Then, when drawing heads, take some tracing paper, or lightbox, or put a layer on top of you are drawing digitally, and try to construct the Reilly rhythms of the head you just drew.
The purpose is to find mistakes in the construction of your sketch. Then put a sheet of paper over the Reilly rhythm lines, and draw the head again.
Example of caricatures done this way.
You can also invent your own rhythm lines when drawing other things, like the human figure or animals.