It is explained, although in very general terms. Exercise is used to stimulate the body’s “countermeasures” (my word) against neuro-degeneration. Squats are called out here for a few reasons: They’re relatively easy for most people to do, and they seem to do a good job of triggering the “countermeasures”, as best as they can tell.
This is not a prescription to drop your exercise routine and only do squats, it’s really just pointing out that squats are a good first choice for sedentary people who want to keep their brains healthy.