Shouldn't the title be lying on the couch, not laying on the couch. Of course, if you're a hen or someone about to have a carnal experience, laying may be more appropriate. As for the origin of the psychiatric couch, some jokesters believe it came from the popular phrase all American GIs memorized in both World War I and II, just before embarking for duty in France: "Voulez-vous couchez avec moi ce soir?" Of course, that encouchment had a whole 'nother meaning than psychiatry.
Whatever the grammatically correct term, spending your expensive hour flat on your back in the psychiatrist's office has various aspects of significance. Since Sigmund Freud led his first patient to the first couch (still on exhibit in London's Freud museum), more than a century ago, those in the profession who followed in his concepts of the profession have considered it essential to the healing process.
As Freud and his advocates insist, the relaxed, prone patient feels secure enough to express anxious thoughts, confusing relationships and fears of mental illness. As the certifiably mad Prince Hamlet pondered, " whether 'tis nobler in the mind to suffer the slings and arrows of outrageous fortune, or to take arms against a sea of troubles." Maybe he wouldn't have been so mad if he had a couch and a Freudian around to help him.
Another factor is the placement of the couch. The patient faces up to the ceiling, instead of engaging in eye-to-eye contact with the psychiatrist. It is thought that inhibitions and shame are easier to cast aside, and the patient feels free to talk without any barriers, nor the embarrassment of having to see the psychiatrist's reactions.