What has Hermia done for which she asks Theseus's pardon? (line 60)
What she has done is to talk back to Theseus who is, after all, the ruler. She is arguing with him over whether she should do what her dad says she has to do (marry Demetrius).
In the part before she asks his pardon, Theseus tells Hermia that her father should be like a god to her -- that she should do whatever he says. Besides, says Theseus, Demetrius is a "worthy gentleman"
At that point, Hermia starts talking back. She says Lysander is as good as Demetrius and that she wishes that her dad would see things through her eyes. Then she asks Theseus' pardon and finds out from him what will happen if she disobeys.