Agitha is by far one of the most bizarre and eccentric characters Link meets during his adventures in Twilight Princess, and me and Flat have been convinced for a long time that she is more important than she appears to be. However, Agitha's dialogue is somewhat disappointing in this aspect, giving us very little to go on. But being the ever-vigilant researchers we are, we thought up a far more interesting and unconventional way of gleaning information from her: Dream Analysis.
Agitha sends you a letter describing a dream she had, which is transcribed in it's entirety below.
Agitha had a dream last night.
Butterflies surrounded Agitha and lifted her up to the sky.
As she waved to the people below in Castle Town, she could see so many people, some waving back, others staring wide-eyed.
Agitha flew in a big circle above Hyrule Field and the butterflies formed into a bed beneath her and said "Let's play again..." Soon they faded away and she woke up in her own bed.
Ohh... Agitha wants so badly to fly in the sky...
Method 1: The Giant Book of Dreams - No noted author, published by Magpie Books
Butterflies
To see a butterfly among flowers and green grasses indicates prosperity and fair attainments.
To see them flying about denotes news from absent friends by letter, or from someone who has seen them.
To a young woman, a happy love, culminating in a life union.
Flying
To fly in a dream often signifies an attempt to rise above your conflicts and difficulties. You need to rise higher but, alas, flights in dreams often end unhappily. Dreamers fly because they are anxious about finding themselves on the ground - flying often represents a flight from yourself.
Method 2: Sharp's Analysis, loosely based in the Freudian Method
This analysis is rooted in the idea that butterflies represent Agitha's money, and perhaps her aristocratic family as well. Agitha first mentions that she is surrounded by butterflies, a reference to the size and value of her fortune, literally being surrounded by money and wealth. She then mentions being lifted above above Castle Town, and circling around in Hyrule Field, both of which signify her feelings of exclusion and alienation from her fellow townspeople. Some of them wave at her, but many just stand there and stare wide-eyed, seeing her as more of an anomaly or a freak than a friend. The butterflies then form into a bed, and tell her they want to play again, both of which are signs that Agitha feels comforted by her fortune, and that perhaps she is happiest when "playing" with it by spending frivilously, but the butterflies then vanish, reminding her that her fortune is not going to last for ever. Finally, Agitha mentions her desire to fly in the sky, which is a thinly disguised way of saying she would like to leave all her troubles behind some day.
Method 3: Flat's Idea
Well I think that Agitha has a little cruuuushhhh! I would say the the butterflies in her dream of yonder night represent Link, and the butterflies he puts in her chest! Link surrounds her and lifts her up, where she can see the people of Castle Town waving and staring, and then he forms the bed beneath her for her to safely return to her Castle. See? It's flawless. She wants to fly again because she wants to be with Link again, which is why she's sending him around collecting bugs for her in the first place. Remember: she wants everyone at her ball to have a partner! She however, is all alone for her ball, how sad! Recapitulating, Princess Agitha's dream represents her longing for Link to be her Prince.
Other Ideas
The entire concept of flying above Hyrule could be a reference to the Oocca. In this interpretation, the people waving are the few Hylians who still remember the Sky People, and the ones staring wide-eyed, obviously less familiar, are the ones who don't.
Marin was another young girl who wanted to fly away from home.
Of course, this could just be more of Agitha's usual bug obsession as well.
Well, there you have it, a ridiculously in-depth look at a seemingly unimportant part of Twilight Princess. Stay tuned for more!