Because the scarlet letter is a symbol, it acquires different meanings for various people, and its denotation changes at different times. It is initially a mark of ignominy and sin, the symbol of an adulteress, and it causes its wearer great shame. When Hester Prynne first appears on the scaffold, she wears the scarlet letter of adultery that she has sewn herself with a certain defiance. 

On the breast of her gown, in fine red cloth, surrounded with an elaborate embroidery and fantastic flourishes of gold thread, appeared the letter A. It was so artistically done, and with so much fertility and gorgeous luxuriance of fancy, that it had all the effect of a last and fitting decoration to the apparel which she wore...but greatly beyond what was allowed by the sumptuary regulations of the colony. (Ch.2)

This letter represents Pearl, the incarnation of her sin; it also denotes Hester's artistry, and it suggests her rebellion against the stringency of the Puritan community. Little Pearl loves this letter, and she tosses wildflowers at it in play. To Pearl, the letter is part of her mother's identity. When her mother temporarily removes this letter while they are in the forest with the Reverend Dimmesdale, Pearl refuses to cross a brook and come to her mother. She demands that her mother replace the letter upon her bosom. Her demand may partly be made because Hester has let her hair fall as she has removed her cap along with the letter, and she now appears to be young and beautiful again. This change in Hester may cause little Pearl to feel disconnected from her mother.

For the villagers, also, the meaning of the scarlet letter becomes altered. At first, it denotes an adulteress, but later many have come to know the A as signifying the word "Able" because Hester tends the sick, she aids the elderly, and she sits with the dying and comforts them. Despite the rewards of her charitableness, Hester has, nevertheless, suffered from wearing the scarlet letter. 

The scarlet letter was her passport into regions where other women dared not tread. Shame, Despair, Solitude! These had been her teachers,--stern and wild ones,--and they had made her strong, but taught her much amiss. (Ch.18)

After Hester Prynne leaves the community with Pearl, she returns some years later wearing the scarlet letter. She returns to "a more real life" in New England than that where Pearl lives.

The scarlet letter ceased to be a stigma which attracted the world's scorn and bitterness, and became a type of something to be sorrowed over, and looked upon with awe, and with reverence, too. (Ch.24) 

The scarlet letter has, indeed, come to define Hester Prynne.