It's so vague to me and I don't understand it. Why is the symbol "scarlet letter" significant?
"There would have been no scandal, indeed, nor peril to the holy whiteness of the clergyman's good fame, had she visited him in his own study; where many a penitent, ere now, had confessed sins of perhaps as deep a die as the one betokened by the scarlet letter.
The scarlet letter that Hester wears on her chest is the very symbol upon which the novel is based. It represents not only the word "adultery" but her public shame in having conceived a child outside of wedlock in a Puritan society. She must wear the letter on her plain clothing daily and show the entire society that she committed a grave sin and is now paying the price. Beyond that the letter is a crimson red color which, later in the novel, comes to correspond with Dimmesdale's own self-inflicted bloody scarlet letter on his bare skin. Though no one but Hester, and then Chillingworth, know the truth, Dimmesdale still punishes himself because he cannot bear the weight of the guilt having to watch Hester suffer alone while he continues to live a relatively normal life without loss of respect from the town.
The Puritans were known to dress in usually dark and dull colors. The red color of the letter would definitely stand out in the town as Hester walked through. Moreover, the color also represents the passion, sin, and guilt that earned her the letter in the first place.
My "answer" is more of a suggestion, so don't use it on any exams. But, since you asked...
On one level the scarlet letter symbolizes Puritan society's judgment of Hester. The Puritans believe the letter stands for "adultery" or "adulteress." Other characters think it could stand for the word "able." Right away, Hawthorne is showing how ambiguous Puritan society's judgment is.
Hester, at first, refuses to accept the letter and the social stigma it signifies. At the novel's end, she returns to Boston and re-affixes the letter to her chest in what seems a combination of penance and acceptance.
So I think the scarlet letter is a symbol of society's judgment of Hester. Hawthorne shows how sometimes society's judgment of people is wrong and false. However, he shows how sometimes society's judgment is right and an individual's self-perception might be wrong. Hester is right in hating the Puritans for their life-hating coldness and hypocrisy, but she ultimately has to accept their judgment in part because her decisions have led to difficult consequences for her and Pearl--and arguably for Dimmesdale and Chillingworth as well, though they're harder to sympathize with.
The meaning of the scarlet letter is ambiguous and "slippery" because the relationship that it symbolizes--between public conformity and individual freedom--is slippery and ambiguous as well.