The essay discusses the relationship between bright, colorful objects, geometric designs, psychoactives, art, and profound experience.
Huxley uses the term antipodes to describe the "regions of the mind" that one can reach via meditation, vitamin deficiencies, self-flagellation, fasting, sleep deprivation, or (most effectively, he says) with the aid of certain chemical substances like LSD or mescaline.
Essentially, Huxley defines these "antipodes" of the mind as mental states that one may reach when certain parts of one's brain are disabled (namely the parts associated with filtering information and signals entering the brain) and can then be conscious of certain "regions of the mind" that one would otherwise never be able to pay attention to, due to the lack of biological/utilitarian usefulness.
For example, he says that the Medieval Christians frequently experienced "visions" of Heaven and Hell during the winter, when their diets were severely hampered by lack of critical nutrients in their food supplies (vitamin B, vitamin C)—these people frequently contracted Scurvy and other deficiencies, causing them to hallucinate.
He also said that Christians and other religions fast in order to make themselves delirious, thus inducing visions and views of these "antipodes of the mind".