Check out The Scarlet Letter's study guide here on eNotes. It expands upon a lot of analytical details that will help you find your answers right away.
The scarlet letter is meant to be a symbol of humiliation, subjugation, and a reminder of the canon of Puritanism. Since Hester was found guilty of being an adulteress, the magistrates feel that they had the right to single her out and render her vulnerable to the insults and judgement of the villagers, who are actually quite ruthless and heartless.
Yet, in their small mind mentality, the villagers grossly miscalculated a very important factor: Hester is an outsider who came to live in the village not that long ago when she was sent there from England by her husband. The latter never made it and was presumed to be dead. Therefore, for all we know, Hester may have come with a completely different set of thoughts and beliefs that distance her completely from the villagers of Boston.
We learn as readers that Hester's husband was taken prisoner by the natives, lived in the wilderness for a while, and then finally came to Boston under the adopted persona of Roger Chillingworth.
[Hester is] the wife of a certain learned man, [who] was minded to cross over and cast in his lot with us of the Massachusetts [so] he sent his wife before him, remaining himself to look after some necessary affairs.
And, from what we know, Hester has only been in Boston for about two years with no news of her husband.
This said, we have to be very careful and not assume that the scarlet letter meant "shame" for Hester. Hester has very little in common with the Bostonians. Otherwise, would a proper Puritan "goodwife" let her desires take a hold of herself to the point of getting pregnant from the saintly man of the village?
On the contrary, the scarlet letter, which meant to put Hester to shame, becomes Hester's very own symbol of individuality. Hester goes as far as designing her very own letter. She embellishes and decorates it to the point that it looked
... fantastically embroidered and illuminated upon her bosom. It had the effect of a spell, taking her out of the ordinary relations with humanity, and enclosing her in a sphere by herself.
Hester's scarlet letter is a declaration of her individuality, personal independence, and the marked desire to separate herself from a society that will never understand her.
Eventually, Hester works so hard on her own that she makes a name for herself as a seamstress. She creates beautiful garments for people, even for those who shun her and insulted her. The scarlet letter changes into different meanings for many people—some go as far as saying that the "A" stood for "able."
The letter was the symbol of her calling [...] many people refused to interpret the scarlet A by its original signification. They said that it meant Able, so strong was
The letter was the symbol of her calling [...] many people refused to interpret the scarlet A by its original signification. They said that it meant Able, so strong wasHester Prynne, with a woman’s strength.
Hester Prynne is aware of what the villagers think about what wearing the scarlet letter will do to her. Yet, Hester sees no shame in her letter, even if she abides by the mandate to wear it as a symbol of shame.
According to the book Understanding the Scarlet Letter: A Student Casebook to Issues, Sources, and Historical Documents by Claudia Durst Johnson (1995), Pearl can be seen as the embodiment of the scarlet letter because she and the letter are the visual reminder of the "indiscretions" of Hester Prynne.
If you think about it, had Hester not become pregnant, she would have never been caught, and she would have never had to wear that pathetic letter on her bosom. Pearl seems to have come to burst the bubble of what once was a passionate, carefree love. She turned the fantasy into punishment. She is the cause of the scarlet letter. The text evidence of this can be found in chapter 7, titled "The Governor's Hall:"
[...] it was a remarkable attribute [...] the child's whole appearance, that it irresistibly and inevitably reminded the beholder of the token which Hester Prynne was doomed to wear upon her bosom. It was the scarlet letter in another form; the scarlet letter endowed with life!
Pearl is also obsessed with the scarlet letter. She teases her mother about it, asking her questions about what it really means. She tries to understand the origin of the letter no differently than she consistently asks about Dimmesdale, as if in aims to understand her very own origin as well.
The scarlet letter has a different meaning for Arthur Dimmesdale. He is actually the one who takes the scarlet letter as a symbol of shame. He is, literally, the only one wearing the letter out of pure shame and guilt. To make matters worse, he is wearing the letter in secret and in the worst way possible: carved on his chest. This is done as self-inflicted punishment since he feels the shame and guilt of not daring to tell his parishioners that it was he who impregnated the “adultress” Hester Prynne; that he has been a hypocrite to his people ever since he first dared to point a finger at her on the scaffold accusing her of the very “sin” that he helped her commit.
He punishes himself over and over for this, but the real punishment that he needs to endure is telling the truth. He is unable to do so and, therefore, he continues to suffer.
Finally, the scarlet letter means a triumph for Roger Chillingworth. Witnessing Hester at the scaffold wearing the letter in shame emboldens him to carry out his revenge against both Hester and Dimmesdale. It is not easy to break Hester, except with threats. Eventually, he needs ultimate proof that Dimmesdale is directly responsible for what happened to Hester: proof to show that “the young divine” is everything but.
Posing as Arthur Dimmesdale’s personal healer under a false name, Roger Chillingworth discovers the carving on the priest’s chest, finally making the ultimate connection. Chillingworth uses the knowledge of the scarlet letter as his personal way to manipulate Dimmesdale into weakness.