While walking through the mall recently, I was struck by the proliferation of Elsa-related items, a good year after Frozen's release. I've read in multiple places that the insane popularity of the movie and her character surprised everyone, even Disney itself, and when I looked at the pictures on the merchandise, I could see both why they were surprised and why girls love her so much.
Look at any Elsa image. She is supremely confident, looking directly out at the viewer with an eyebrow raised. She is powerful, and knows it. She's not a princess, she's the freaking Queen. She has a power that can take anyone down. Most other princesses are sweet, curious, smart, helpful, strong-willed, but they are almost always victims of circumstance who, in most cases, end up needing to be saved by a man. Elsa IS the circumstance. She's a force of nature. She embraces her power, and refuses to tame it. Her only weakness is the sister she loves. In a sense, her character is closer to Maleficent than any other Princess.
Why wouldn't girls want to be her? The average young girl is basically helpless. Taken care of by her parents, told about the constant dangers in the world, and living a completely controlled existence. This isn't a bad thing. However, doesn't it make sense that those young girls fantasize about making their own decisions and having the power to flick away any annoyances? Elsa is the first Disney woman I can think of to achieve that. What's not to love?