In “Young Goodman Brown” by Nathaniel Hawthorne, what do the woods symbolize? How do they function in the story, and how do they guide the overall meaning of the story?

Hawthorne's "Young Goodman Brown" is a short story about a man living in a Puritan community which he believes to be inhabited by virtuous people. This is symbolized particularly by his wife, Faith, who represents the faith Goodman Brown has in his family and friends as being righteous; Hawthorne notes that she is "aptly named." As Brown sets off on his journey, however, "twixt now and sunrise" he will discover in the forest that all is not as it seems.
In leaving behind Faith, whom Brown believes to be "a blessed angel on earth," and setting out toward his "present evil purpose," Brown leaves behind the open community of the town for "a dreary road, darkened by all the gloomiest trees of the forest." There is a clear symbolic divide between the clearing of the town and the ominous grip of the forest, which marks the place where the known ends and the unknown begins—or so Brown thinks.
Having entered the forest, the trees "closed immediately behind" Brown. If we understand the forest to represent evil and the unknown, this suggests that, having stepped into evil and begun to discover what is unknown, we can never return—the forest has enclosed Brown.
The woodlands were believed by the Puritans—and, indeed, by many Christians in the seventeenth century—to be the habitat of the devil, cast out of townships and into the confusion of trees. Appropriately, Brown fears that "the devil himself" might be "at [his] elbow" as he progresses deeper into the forest, further away from the safety of the known.
As Brown gets deeper into the forest, the symbolism of Satan intensifies. The traveller he meets has a staff "which bore the likeness of a great black snake," which seems to writhe in front of Brown's eyes. Later, "he of the serpent" encourages Brown to continue on into the forest, which Brown thinks is unChristian—"my father never went into the woods on such an errand." But the traveller tells Brown that he is incorrect in his assumptions and that his father before him had taken this path. The suggestion here is that those Brown thought to be pure and honest Christians have in fact trodden the paths of evil, as represented by the forest.
As Brown journeys deeper "into the heathen wilderness," he sees more and more people he believed to be "holy" also traveling there. Eventually, the forest becomes "peopled with frightful sounds," until Brown himself begins to run "demoniac" through the forest, as if taunting the evil to respond to him. As the "benighted wilderness" calls out to him, it takes on a life of its own, the embodiment of evil. It is at the very heart of this most thick and horrifying forest that Goodman finds the host of his community gathered, apparently conducting an appeal to Satan. Even Faith is there, "before that unhallowed altar." At the thickest heart of the forest is the greatest evil concealed, and, having seen this, Goodman Brown can never forget it.
After the story reaches its climax, Brown does return to the village. There he finds the town going on exactly as it had before, but Brown is changed. Although he questions whether he has only dreamed the horrors of the forest, he no longer believes in the piety of his community. Having journeyed into the evil represented by the forest, led by Satan, he can only return as a hypocrite to live among other hypocrites, who may pretend to be virtuous but who walk the paths of the forest under cover of night.