What makes the character Hermia so compelling, and how is she important in the play?
hmm...that's an interesting question, because i think that Shakespeare wrote the play so that Hermia would not be so compelling: she is interchangeable with Helena basically. All of the main characters are similar, which is what adds to the confusion that ensues. Although i'm sure Lysander wouldn't agree that she's the same as Helena, the audience probably would.
If you really want to argue it, I guess you could say that Hermia is strong. She says that she doesn't know "by what power I am made bold'' (I.i), but clearly she is so when she asks what happens if she refuses her father's wishes for her to marry Demetrius. You could also mention that she is virtuous, as she refuses to sleep next to Lysander once they've reached the forest.
I would agree that Shakespeare wrote the four lovers to be interchangeable; however, I do think there is one compelling element about Hermia: she is wanted by both of our young men. I think that that's what makes her stand out a little bit. Although we, as an audience, don't really know what it is about her, there must be something that causes the attraction of both men and leaves poor Helena in the cold.
She's important in terms of the plot because it's her decision that forces the action of the entire play. She chooses to not listen to her father which leads to Herm and Lys running off to the woods where the tradesmen happened to be practicing....and hilarity ensues...