What does Pearl Prynne need in The Scarlet Letter?
Hester's daughter, Pearl, needs her father to acknowledge her. Until he does, she exists only as a symbol: of her parents' love, their sin, their secret, her father's guilt, her mother's scarlet "A." She cannot really be a person because her lack of this link to the world leaves her somewhat untethered. It's as though her self is too open to interpretation until she is claimed. Once Dimmesdale, her father, finally publicly acknowledges her upon the scaffold before all his confused parishioners, only then can she become a real individual and lose her symbolic status. The narrator says,
Pearl kissed his lips. A spell was broken. The great scene of grief, in which the wild infant bore a part, had developed all her sympathies; and as her tears fell upon her father's cheek, they were the pledge that she would grow up amid human joy and sorrow, nor forever do battle with the world, but be a woman in it. Towards her mother, too, Pearl's errand as a messenger of anguish was all fulfilled.
Therefore, in order to have a real life, a life in which Pearl no longer fights society as an enemy, real or imagined, Dimmesdale had to acknowledge her. In order for Pearl to become a person instead of a symbol, she had to be publicly claimed by him.