In Nathaniel Hawthorne's "Young Goodman Brown," the literal path Brown takes is that which carries him away from his home and his new wife, into and through the forest on some unidentified errand. Along the way he meets an old man who walks with him, and others from the town pass by as well.
However, the literal path is not the one that carries the story's true message. The figurative the path is symbolic of the path one chooses to take in life. Hawthorne is presenting a picture of following an upright, moral path, or a path of sin. It is a part of the human condition that each person makes such a choice, maybe without even realizing it—which road to follow?
In this story, the path is not littered with temptations as one might expect, but by the presence of people Brown knows. His own outlook on life seems too weak to withstand the imperfections of others. When he realizes that others are sinful, it does not motivate him to lead a more virtuous life, but turns his heart into a cold, hard thing inside that feels no charity, no forgiveness for other sinners (as it seems he forgets to include himself as a sinner), and he becomes anything but the loving person the Bible teaches he should be. The author alludes to the Puritans with his tale—they showed no sympathy, no support, and no concern for one another. They were inflexible and judgmental, and were responsible for the Salem Witch Trials.
Literally, Brown is taking a walk. Figuratively, he is walking a path where his destination does not depend on where he places his feet, but where others place theirs, following not God, but imperfect people, and losing faith because he does so.