The scarlet letter A is a symbol of public shame. Hester is made to wear it so that everyone who sees her might know the nature of her sin and shun her. The fact that she has publicly confessed and received punishment means that Hester is able to move on with her life and proceed to try to make up for what she has done. Meanwhile, Dimmsdale, who has not confessed and therefore has no scarlet letter to show the world, is stuck with the agony of his guilt and is unable to enter the stages of redemption.
The Scarlet Letter 'A' symbolises not just one or two aspects but many. First as regards character it symbolises fiery Nature of Pearl, then it refers to different meanings regarding Hester's Character, on the initial state it stands for Adultrous, then later on it refers to her Angelsome character when she overcomes all her troubles.