The only way to find it out is to read the novel, which is bound to tell you more about it sooner or later.
"A Thousand Pieces of You" is a science fiction or fantasy novel.
From a Google search I found a link to an excerpt.
"The Firebird" is capitalized. It is a proper name.
"The Firebird" is some kind of device, charm, or amulet that can carry the bearer "across dimensions" into other parallel universes.
There's no doubt in my mind that it's supposed to evoke the image of the mythological bird. If nothing else, it calls to mind the Pontiac sportscar which featured an image of a "firebird" on its hood. The cross-dimensional transport gadget probably looks something like this: