The Firebird is a magic bird that brings music to all of Russia.
Rocket's Firebird Rescue
In the story, Firebird was responsible for bringing all the music in Russia and always got away from Katschai. When Katschai finally captured her, he locked her up in a birdcage where she couldn't bring or make any music. Eventually, she was rescued by the Little Einsteins and went back to her duties.
Despite her color, she has nothing to do with fire.
When one of her feathers were taken off, you can use her power for music.