What is the significance of the "A" throughout the story? Scarlet Letter by Nathiel Hawthorne

THE STORY OF THE SCARLET LETTER Condemned to wear a bright red "A" over her breast wherever she went, Hester Prynne had been convicted of adultery by Boston's Puritan leaders because she gave birth to a boy while her husband had been away. Emerging from the prison house with everyone in the town watching, Hester was led to the town square and walked onto a scaffold with her baby in her arms. There on the …

…his hand to Hester, Dimmesdale admitted to his sin, and condemned himself for the years he had lived in sin. Then he focused on Roger Chillingsworth and exposed the true identity and evil nature of the man. With his sin finally confessed he collapsed on the scaffold. Dimmesdale then said his goodbyes to Hester and Pearl. Then Pearl kissed him of the cheek with really showed that she did love him. Finally, Dimmesdale passed on.