Could you help me understand the quote from The Scarlet Letter below?
"It is remarkable, that persons who speculate the most boldly often conform with the most perfect quietude to the external regulations of society."
Real quick, you have to understand that The Scarlet Letter (being about a sin in the Puritan population) is going to deal with some matters that are highly spiritual. These matters refer to an on-going contrast between good and evil, angels and demons, and God and the Devil.
This sentence is a topic sentence of a new paragraph that is indicating a transition into a new topic. The previous paragraph cites the word "speculation" which in context means that Hester was free to think. (Free thinking wouldn't have been common for Puritans... Bible, bible, bible was more their way) Before the quote you cite, the text says:
"In her lonesome cottage... thoughts visited her, such as dared to enter no other dwelling in New England; shadowy guests, that would have been as perilous as demons to their entertainer, could they have been seen so much as knocking at her door."
This quote refers to evil thought, it almost calls them demons but doesn't. The fact that these thoughts were almost visible or capable of knocking at her door demonstrates how real it felt to her.
Then the quote you cite was written. Her speculating or wondering about the other world, the spiritual world for good or for evil was done with great boldness. She did not fear it. If God or Satan tried to talk audibly with most anyone today it would scare us to death. But, she didn't let on that she had these moments. In fact, she "conform[ed] with the most perfect quietude" to the regular events going on in the society. She continued about her way as if there was no real and present spiritual world that affected her.
After your quote, Hawthorne goes on to write about how this tangibly shakes out in the obviously spiritually afflicted Pearl that Hester has to wrestle with on a daily basis.
In short, Hester has some inner demons she fights with, but she works really hard to keep that to herself and not reveal it to society.