This is Hermia and she loves Lysander just as much as Lysander loves her, but because the law of Athens sates that women has to listen to who their father wants them to marry. Since their love is unbreakable they both decide to run to Theseus's aunt's house in the woods. If they decide to get married in Athens Hermia will have to choose to be executed or become a nun and never see a man again.
This is Lysander and he is Hermia's boyfriend. He thinks of a plan to run into the woods to his aunt's house, so both of them can get married and Hermia will not have to be executed or become a nun. They plan to go to the woods the same time that the play characters are supposed to rehearse.
This is Egeus and he wants his daughter Hermia to marry Demetrius, but Hermia refuses. Since Hermia is not listening to him he has Theseus talk to Hermia and he gives her 3 choices. Egeus does not know about Lysander and Hermia's plan to run away so he thinks that Theseus will talk Hermea into marrying Demetrius.