In "Young Goodman Brown," the satanic imagery complements the dark, dreary oppressiveness of the forest itself, which in turn complements the inner darkness that Goodman Brown discovers in the human psyche.
"Young Goodman Brown" is a story about an encounter with evil, centered around an epiphany of sorts, as Goodman Brown comes away from his experience in the forest with a newfound awareness on the nature of sin, even as he is also destroyed by that awareness.
In this, Goodman Brown's journey is simultaneously a journey outwards, away from Salem and into the forest, but also a journey inwards, exploring the subject of sin as it exists in the human soul.
Ultimately, both aspects of his journey (the physical journey through the forest and the spiritual journey charting the nature of human sin) lead him to the same place: the Sabbath. Here, note the inclusion of his wife within this ceremony (and the symbolic importance of her inclusion). His wife's name, Faith, is not an accident, as she herself represents Goodman Brown's own faith in other people, and in this, her pending corruption symbolizes the destruction of Goodman Brown's own capacity to place trust in the people around him.