Many traditional explanations of conflict include things like Man vs. Man, Man vs. Nature, but these don't seem appropriate for "Young Goodman Brown." The conflict in this story is between man (Brown) and his unreasonable demands on other people to be what he wants/needs them to be.
You always have to remember that we have no solid evidence that ANYTHING happened in this story; the end seems to suggest that it was all a dream, our "common sense" seems to suggest that it's a dream, but it doesn't make any difference. Brown comes back to town unable to accept what he perceives to be the "evil" in the people he once admired---but there is no evidence that any of them are evil, just not perfect.
So the best conflict may be Man vs. Illusions.
The Enemy of the Good is the Perfect.
(I guess I should use "Person" in all of these :) )
The conflict is the problem in a piece of fictional literature. The story of the background and development of the conflict and the struggle to find its resolution is the reason for the writing of the novel.
A conflict may be between two or more characters, between different aspects of one character's own personality, or between a character and an external condition or situation. In Moby Dick, for example, one major conflict is the search for revenge waged by Captain Ahab against the great white whale. In The Call of the Wild, one of the areas of conflict is the battle for survival of men and animals against the harsh climate of the Arctic. In many works of science fiction, the conflict arises between humans and computers, robots, or other forms of artificial intelligence.
In “Young Goodman Brown,” the protagonist is the title character. The antagonist is ostensibly the devil, the spirit resembling his father (paragraph 13), although the antagonist might also be Brown’s destructive sense of guilt—his projection of his own sinfulness upon others and his consequent damnation of them. The central conflict of the story, which seems lost even before it begins, is within Brown himself: an inner war of love and trust versus suspicion and distrust. The resolution occurs after Brown’s climactic denial in paragraph 68. Brown’s life is changed after this because his faith in others has been shattered, and therefore he alienates everyone around him.