Psychoanalysis is a form of psychotherapy developed by Sigmund Freud. In his model, id, ego, and superego are three parts of the mind: https://en.wikipedia.org/wiki/Id,_ego_and_super-ego . From that article, the id "contains a human's basic, instinctual drives," particularly sexual and aggressive drives. In a healthy psyche it is balanced and held in check by the superego and ego. A "veneer" is literally a thin layer of wood--a thin layer of beautiful wood providing a beautiful surface to hide the cheap-looking wood underneath. People often use "veneer" figuratively--"a thin veneer of civilization over our primitive selves." "Free association" is therapeutic technique of encouraging the patient to let one idea lead into another, in hopes that they will get around to talking about the things that are really bothering them but which are too painful to approach directly. The passage says that psychoanalysis has to be done carefully and takes time. If Judd tried to work quickly, instead of leading to insight that could help Judd treat Burke, the "free association" might damage Burke by taking him too quickly into areas Burke was not ready to talk about, resulting in "the thin veneer of the id... [blowing] wide open."