The music has a light and delicate quality that Akiko and her team obviously connected to the idea of a bird in some way. The music builds and then soars at the end...you could also relate that to a bird in flight if you just have to have something to tie everything together.
Art can be abstract and, for me, it's what makes this program stand out from the rest of the Black Swans, Carmens, Les Mises, Delilahs and other oft-used pieces that come with a ready-made story. If you need to grasp a concept to understand or, at the very least, enjoy a program like this then it's obvious you don't get it and that's fine. But just b/c you don't understand it doesn't make it less than what it is.