Hester has heard that the Governor is thinking about taking Pearl away from her. She goes in order to argue against this idea. The idea is that Pearl is getting a little out of control and could likely use a little better supervision. There is notice in Pearl that some evil spiritual activity might be at work. Perhaps this is evidence of the father according to the magistrates who discuss these circumstances. The concern of witchcraft is never fully determined. The ultimate decision is to let Pearl stay with Hester. Thus, Hester's pleas and Dimmsdale's support helped ensure that she keep her child.
On a side note, Hester did bring the governor some gloves that she had embroidered for him.