What do we know about Mr. Hooper in "The Minister's Black Veil"?
We know that he has a reputation for being "good" as he is called "good Parson Hooper" or "good Mr. Hooper" often by both townspeople and the narrator. Further, the narrator tells us that
Mr. Hooper had the reputation of a good preacher, but not an energetic one: he strove to win his people heavenward by mild, persuasive influences, rather than drive them thither by the thunders of the Word.
In other words, he is no "fire-and-brimstone" minister. He doesn't try to scare his congregation into right or moral behavior; instead he has always tried to "win" them over by persuading them of the benefits of such behavior.
Moreover, he was engaged to a woman named Elizabeth at the start of the story. However, when he refuses to directly explain to her the meaning of the black veil, or to show her his face once more after she figures it out, she leaves him.
Finally, we know that Mr. Hooper has some secrets. He tells Elizabeth, "'If I hide my face for sorrow, there is cause enough, [...] and if I cover it for secret sin, what mortal might not do the same?'" In this way, readers indirectly discover that Mr. Hooper wears the veil in order to symbolize the way every person attempts to hide their true, sinful natures from their fellows. He wears the veil to hide his face just as we all wear a figurative veil to hide our souls. Even on his deathbed, Mr. Hooper will not remove the material veil. He asks,
"Why do you tremble at me alone? [...] Tremble also at each other! [....] When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I have lived, and die! I look around me, and, low! on every visage a Black Veil!"
This confirms what he'd told Elizabeth. ALL of us hold up a figurative veil to hide the true content of our souls from everyone else, even those we love. This is why Mr. Hooper says that he sees a black veil on every face. Thus, we do not know what secret sins Mr. Hooper harbors, but we do know that he is a sinner, just like everyone else.