Even though the couch may largely be the stuff of Freud and a few radical hangers-on, should you find yourself faced with "the couch" go ahead and lie down, flat-out luxuriate because when your body is relaxed your mind relaxes, thoughts come more freely. When people rest, their self-censors rest too. Consequently, they may be more honest when they talk. Beyond that, when someone lays down they are symbolically saying to their therapists, "I trust you." A trusting relationship fosters honest communication.
The other point of significance is that "the couch" is a symbol of the power differential that exists between patient and psychoanalyst. The idea that the patient is giving another person the job of decoding his or her thoughts. So psychoanalyst walks the tightrope between being the one with the power and being the one with the power to heal.
Still another point of significance, is the symbolism of sickness. It is almost as if when the patient lays down the psychoanalyst is tending to the patient's psychic wounds.
The significance of "the couch" can sometimes be over-analyzed (go figure!)to the point of creating a whole lot of expectancy and worry in the would-be patient. The important thing to remember is, sometimes a couch is just a couch.