The only "answer" that Elizabeth is given from Hooper as to why he has donned this curious veil is one that does not really explain fully the complex reasons for Hooper's dramatic fashion statement. Note what he says to Elizabeth:
"Know, then, that this veil is a type and a symbol, and I am bound to wear it ever, both in light and darkness, in solitude and before the gaze of multitudes, and as with strangers, so with my familiar friends. No mortal eye will see it withdrawn. This dismal shade must separate me from the world: Even you, Elizabeth, can never come behind it!"
Of course, we are not told at this stage in this excellent story precisely what the symbol of the black veil is as it is interpreted by Hooper. However, the vow he has taken to wear it seems to be a personal one that reflects Hooper's awareness of his own sins and his fear of presenting himself as a sinless hypocrite. The veil acts as a constant reminder of his many sins that separate him from others and from God, as Hooper's death-bed confession suggests that the veil is only physical symbol of what is a metaphorical reality for everyone, for all of us have our own black veil of sin that acts as a barrier in our relationships with others and with God.
The day that the minister showed himself wearing the veil, he made the statement that he was wearing the veil to represent his unseen sins. He then gave a more powerful sermon than he had ever done before. The effect was significant on others and he ahd felt the power of his voice.
The minister seems to keep the veil on because he sincerely believes that the sins he carries within him are ugly and should not be seen. We are all familiar with our outward sins that others may see, but it is the secret ones that we have to work on. For this reason he has to keep the veil on his face, because he sins.