One token of her shame is her child, an apparent proof of her infidelity to her husband, who had been gone for long. Another token is the scarlet letter A, embroidered on her chest. It stands for "Adultery", as a shameful mark of the public condam.nation. First, she tries to conceal the letter, but then she realizes it isn't possible, and decides to reveal it.
The fact that this letter is beautifully embroidered, in spite of its meaning, tells us that she will live up to the challenge, and eventually find a way to clear her reputation.
