Plain English Meaning
Medicines that calm the mind or nerves. They slow you down mentally, which is fine on the ground but unsafe in the cockpit.
Full Definition
A class of medications used to reduce anxiety, calm nervousness, or treat psychiatric conditions such as depression and psychosis. Tranquilizers act on the central nervous system and can impair alertness, reaction time, judgment, and coordination — all of which are required for safe flight. Their use, and in many cases the underlying condition being treated, can disqualify a pilot from flying under FAA medical standards.