According to The Book of Knowledge: The Keys of Enoch by J.J Hurtak, Key 3.1.7,

“The axial lines are part of a fifth dimensional circulatory system combining color and sound, which are used to draw from the Overself body the basic energy used  for the renewing functions of the human evolutionary body. Conversely, axiatonal lines operate prior to the action potential for the animation of the human species. Furthermore, they bring together the all-important tonal vibrations governing each axis and all ultrasonic activities connected with the colors of Healing® that relate to each tone and multiples thereof. Hence, the axiatonal lines can be used for the complete regeneration of an organ…”

I recommend people who are interested in the source material from which Reconnective Healing and the Reconnection stem to explore the Book of Knowledge: The Keys of Enoch by J. J. Hurtak.  In particular, Reconnective Healing and the Reconnection are associated with Keys 3.1.7 and 3.1.4.

Another explanation of axiatonal grids is found in Esoteric Acupuncture by Dr. Mikio Sankey. According to Dr. Sankey, “There exists a massive interconnected grid work pattern, or systematized [energy] flow throughout the entire solar system connecting all of the stars and planets together throughout our universe. This interconnectedness extends to other solar systems outside of our universe…

…axiatonal grids refer to energy pathways arranged in a grid-like manner that are similar to cobwebs, but that exist outside of the energetic force field of each person. Some of the axiatonal grids are close to the surface of the Earth, while others extend outward to connect to various planetary, solar, galactic and other universal systems.”