"In the Minister's Black Veil," the speaker states that one "desirable" effect of the black veil is that makes Mr. Hooper a more "effective" minister. According to the text, the reason for this is simple:
He became a man of awful power over souls that were in agony for sin.
Remember that at the beginning of the story, the congregation is alarmed by the black veil. They regard it as a "terrible thing" that makes Mr. Hooper appear "ghostlike" from his head to his foot. So, for the congregation, the black veil is a visible reminder of the sins they have committed. More importantly, these sins cannot be disguised or forgotten, just as Mr. Hooper's veil cannot be ignored. As such, the black veil forces the congregation to acknowledge their sins.
In addition, by wearing the veil, the congregation no longer view Mr. Hooper as a man above sin. They realize that he is mortal and that he too has committed sins. This enables Mr. Hooper to be a more effective minister because his congregation can better identify with him.
The narrator says, "Among all its bad influences, the black veil had the one desirable effect, of making its wearer a very efficient clergyman. By the aid of his mysterious emblem--for there was no other apparent cause--he became a man of awful power over souls that were in agony for sin."
This is a very specific kind of clergyman--one very Puritan, and very much in line with other works by Hawthorne. As far as why, there are several reasons. The veil hides his face, allowing sinners to imagine the best and worst. The fact that he carries darkness with him all the time allows them to think of him as one of them: a sinner.
The veil had a positive effect on the ministry of Reverend Hooper. Many people convert to his faith and people want him to be with them when they are on their death beds. Much like the scarlet letter of Hester Prynne, Hooper is thought to have some kind of special understanding about life. The veil makes him seem more mysterious and perhaps, people think, a sinner who will understand their own sinfulness. Unfortunately for Hooper, the veil also separates him from friends and, more especially the love of his life.