I am not sure if you mean the time period Hawthorne wrote "The Scarlet Letter" or the time period in which it was set. I shall try to provide both answers for you.
First, Hawthorne was interested in documents he had come across while reseaching his own ancestors. He discovered that a woman had indeed been branded with a letter "A" as punishment for adultry. Hawthorne became fascinated with the religious hypocrisy of the Puritan era. By the time it reached American shores in the late 1600s, Purtiansim had become a corruption of the original ideals that led to the travesties like the treatment of Hester and eventualy the Salem Witch Trials. Puritanism suffered a severe decline in adherence thereafter.
As for Hawthorne's time, he offers his "Scarlet Letter" partially as a warning to those who would read it in modern times. Crowds can easily become hysterical with little or no basis in reality. For example, on pg 116 (my edition) he writes, "When a multitude atttempts to see with its eyes, it is exceedingly apt to be decieved." Or, later (pg 185), "Prison is in our own minds."
The message, therefore, is that we should not be fooled into thinking the Puritan acts were some sort of abberation. They could, have, and will continue to occur. Just look at the headlines any day of the week...