What secrets of Reverend Hooper does wearing the black veil symbolize?

We don't know for sure as Hawthorne never explicitly gives the reason for the minister's wearing of the black veil. Nevertheless, the veil itself is incredibly symbolic. In wearing it, the minister wants to hammer home the message to his parishioners that sin separates people from each other. Unfortunately for Hooper, many simply don't comprehend what the minister's trying to say by his wearing of the veil. They think that the black veil symbolizes some dark secret or sin for which the minister is trying to atone.
This was Edgar Allan Poe's understanding, too. He believed that the Reverend Hooper wore the veil to express his guilt at committing adultery. He points out that Hooper only started to wear the veil on the day that the lady at the beginning of the story died. Poe's speculative hypothesis also tallies with Hooper's behavior towards his fiancée. He refuses to divulge to her the reasons behind his wearing of the veil; he even refuses to take it off in her presence, leading to the breaking off of their engagement. He literally cannot look her in the eye such is his overwhelming sense of guilt.