Let us remember for one moment the key elements of a plot graph. In order, they are the exposition, which presents the main characters and the conflict, the rising action, in which a series of events heighten this conflict, leading us to the climax, which is the most emotionally engaging section of the story, which leads to the resolution, which is how the story is resolved and the conflict ends.
If we think about these four stages of the plot of "The Minister's Black Veil," the exposition is clearly the sudden arrival of Mr. Hooper in a black veil. The rising action begins with the parishioners wondering why on earth he is wearing it, and this continues when he wears it for both a funeral and a wedding, and then, even at the cost of losing his love, he refuses to take off his black veil at the behest of his fiancee, Elizabeth. This rising action of course leads to the climax, which is Mr. Hooper's stubborn refusal to remove his black veil even on his death bed. This section also gives us a key clue as to the symbolic meaning of the black veil, for Mr. Hooper, when he looks at others, sees a black veil covering every face. Lastly, the resolution would be when Mr. Hooper dies and is buried with the black veil still firmly covering his face.