What is the Birdsong, actually?

The birbs don't realize this, but the force they refer to as "the Birdsong" is a field of nanomachines that permeates Bird-Earth's atmosphere. What the birbs refer to as 'magic' is their ability to use this as a force. 

Birbs have a store of nanomachines that are attuned to their bodies. If a birb were to leave the atmosphere of Bird-Earth, they would find the power of their magic drastically diminish; a birb using its own local nanomachines is a much less powerful magic-user than a birb that is leveraging the entire planet's system of nanomachines.