What is a rumor the townspeople pass around to explain their pastor’s wearing of the black veil?
First, Goodman Gray says that "'Our parson has gone mad!'" and the village physician concurs that "'Something must surely be amiss with Mr. Hooper's intellects [...]." So, they initially whisper to one another that he has actually lost his mind and, in this way, account for the strangeness of the black veil.
Soon, however, Mr. Hooper's unwillingness to see his own reflection in a mirror or pool of water leads his parishioners to say that "Mr. Hooper's conscience tortured him for some great crime too horrible to be entirely concealed, or otherwise than so obscurely intimated." They are correct to associate Mr. Hooper's veil with sinfulness, but they fail to understand (or persuade themselves not to understand) that it concerns more than just his "secret sins," and it refers to their own as well. Readers never find out if there is one significant sin that Mr. Hooper feels compelled to hide or if it is simply his desire to truthfully express what he understands of the human condition. His words on his deathbed indicate the latter.