A psychological reading would say that the "dark forest" is the unconscious where we harbor desires that our superego (the conscience of society--that which helps us distinguish what society says is right from wrong) forbids us to do and our conscious keeps under wraps (so to speak). For Freud, a "dark forest" signifies repressed sexual desires, especially with all the trees functioning as phallic symbols. For Jung, another 20C psychologist (and theorist), the walk would be a journey to and through Brown's "shadow self," which for Jung is a real part of every individual that we deny but need to acknowledge in order to become complete. "Acknowledge" does not mean act upon; it means discover and claim as part of who you are.
Hawthorne had strong objections to the type of social repression encouraged by the Puritans. He wanted to illustrate how social pressure to conform and appear "religious" often created bad results in members of the community. In Goodman Brown, Hawthorne uses the dark forest to symbolize the dark nature of man's soul. The "sinful" desires of the townspeople are explored in the forest. Goodman Brown encounters his neighbors engaging in witchcraft and behaving deviously in the forest. He encounters a character resembling the devil, which is the purest incarnation of the dark side of human nature. Brown himself leaves the forest, but the forest doesn't leave him. He is left with dark thoughts, loses all faith in humanity, and is paranoid and unhappy for the remainder of his life.