The first passage is spoken by one of the old townswoman who stands outside the prison, waiting for Hester to come out. She believes that a young woman who commits a crime should be at the mercy of the older woman of the community. The belief is that women must control their sisters because men are not harsh enough:
“Goodwives,” said a hard-featured dame of fifty, “I'll tell ye a piece of my mind. It would be greatly for the public behoof, if we women, being of mature age and church-members in good repute, should have the handling of such malefactresses as this Hester Prynne. What think ye, gossips? If the hussy stood up for judgment before us five, that are now here in a knot together, would she come off with such a sentence as the worshipful magistrates have awarded? Marry, I trow not!” (Chapter 1)
This next quote discusses Hester's private punishment, that she chose to stay in town because she had to do her penance:
Here, she said to herself, had been the scene of her guilt, and here should be the scene of her earthly punishment; and so, perchance, the torture of her daily shame would at length purge her soul, and work out another purity than that which she had lost; more saint-like, because the result of martyrdom. (Chapter 5)
Hawthorne's message in the book is that no outwardly punishment will ever be effective as the private punishments sinners inflict upon themselves as a result of their sins.