The description of the sunlight running away from Hester occurs in chapter 16, when she is out walking near the forest with her little daughter Pearl. The implication of this seems to be that Hester is carrying a dark secret. The scarlet letter on her breast is the physical sign of her adultery, but she has not revealed the name of the man with whom she had an affair. This man happens to be the minister Dimmesdale, and she wants to protect his name and his career; although, admittedly, Dimmesdale suffers terribly under the weight of this guilty secret. Hester is more resilient but she too suffers mentally. The secret which weighs them both down is not to be dragged into the light. Thus, symbolically, the light itself appears to shun Hester. Under the weight of her sin and punishment, Hester has lost her spontaneity and has become shut up in herself. She has had to suppress her natural instincts, and so the sunlight, a natural element, appears to withdraw from her.
It is Pearl, Hester’s little daughter, the result of her liaison with Dimmesdale, who comments on the sunlight running away from Hester. This is significant, as Pearl is portrayed as a child of nature rather than of the strict Puritan society which condemns her mother. Pearl is completely free and wild, and, as she remarks, the sunlight will not run away from her as it does from Hester. As Hester watches, the sunlight seems of its own accord to mingle freely with Pearl:
The light lingered about the lonely child, as if glad of such a playmate, until her mother had drawn almost nigh enough to step into the magic circle too. (chapter 16)
Pearl is a reminder of what Hester used to be like, going by her instincts and not by the conventional ways of society. Under her influence, Hester too appears to come closer to the ‘magic circle’ of nature and freedom.