The symbolism in Hawthorne’s Young Goodman Brown is mostly of a religious nature. There a mix of the supernatural as well as redemption among other things that are traits of the American Romantic period in which Nathaniel Hawthorne wrote in. Many of Nathaniel Hawthorne’s stories—such as The Scarlet Letter—focused on the hypocrisy of Puritan society, the betrayal of good, and the eventual victory of evil (sometimes disguised as good).
The titular character is seen as representing innocence, which is a trophy that the wicked would love to possess. In his errand in the forest, Brown could be seen as losing his innocence to the old man. One could also look at Young Goodman Brown in the same light as Eve of the Bible. Also, his name implies that he is a good man.
The story takes place in the time of the witch trials. The witches of folklore usually did their deeds and had their sabbath at witching hour in the forest which was believed to be the domain of the Christian devil at the time. Young Goodman Brown’s mysterious errand takes him through the forest where things occur that shakes his beliefs when he returns to reality (or one could say when he leaves the forest).
It is in the forest that he calls to his wife Faith who doesn’t answer him and where he sees all the townspeople gathered for some sort of rite. Since this a Puritan community and the hunting of witches was encouraged, this could be seen as showing the hypocrisy of Puritan society, something Hawthorne was aiming at in Young Goodman Brown. It could also be said that the forest is where Young Goodman Brown is to lose his innocence.
Young Goodman Brown was set in Salem where the 1692 witch trials took place. It was time when many innocents were sentenced to a variety of deaths either when “proven” to be witches or through tests to prove they were. Salem adds a supernatural vibe to the story so everything pretty much fits together as the story goes on.
Faith has been a symbol of virtue, innocence, and trust to Young Goodman Brown. When he sees calls out to her while traveling and she doesn’t respond it could be seen as a loss of faith and virtue. See her as well as the townspeople in the forest at that time of night also cast doubt on the culture and faith he was part of. Her name implies the mentioned traits of innocence and virtue.
The old man’s staff bears a serpent and Brown—representing innocence and all that is good and virtuous—is tempted by staff and uses it to get through the forest quicker. This returns to Young Goodman Brown being similar to Eve.