Before you read this...
Don't read it if you've just started the game, or are going to whine about "spoiling" the game.
I've tried to be very specific without spoiling the game.
It's actually quite simple when you think of logically. When you first meet up with Midna, she says that you may be of some use to her. Later on in the game you meet Zelda. They both speak to each other like they know each other (which they do), but they come to disagreements. Zelda speaks of why the castle is cast into perpetual twilight, you see Zant. He's the Twilight "King." After defeating a few more dungeons Zant speaks to Midna saying that he needs her.
We're almost done kiddos. When you get all three shards of the mirror, the sages call her Princess Midna. DUN DUN DUN. Then she admits that she fled her people because she didn't want to be seen as an imp. Zant could only break the mirror into pieces, this actually plays a vital role in determining who's the twilight princess. Midna says that only the true ruler of the Twilight can break the mirror and she does so in the ending cutscene.
MIDNA IS THE TWILIGHT PRINCESS.