The Phoenix appears to be a critical symbol in Fahrenheit 451 , and previous answers have already provided the key quotation on this (see the quote which begins: "There was a silly damn bird called a Phoenix . . ."). To this, I would note that Bradbury also references the...
The Phoenix appears to be a critical symbol in Fahrenheit 451, and previous answers have already provided the key quotation on this (see the quote which begins: "There was a silly damn bird called a Phoenix . . ."). To this, I would note that Bradbury also references the Phoenix in connection with the firemen (and this isn't insignificant, given the symbology of burning books, along with the image of the phoenix as a burning bird).
As the book opens, when he first encounters Clarisse, she is described as "hypnotized by the salamander on his arm and the phoenix-disc on his chest." Note that these images are quite literally imprinted upon Montag's uniform. Later, Captain Beatty is shown wearing the Phoenix insignia on his hat. I don't think these references are incidental: in many respects, I think the image of the Phoenix is a metaphor which sums up and embodies the core message of Fahrenheit 451, when taken as a whole.
Ultimately, note that Fahrenheit 451 closes on an image of destruction joined with the hope for rebirth. Now, consider that image within the context of the Phoenix mythology itself. In each, death/destruction and birth/creation are closely tied together. The Phoenix dies and is simultaneously reborn from its own ashes. This is precisely what is happening with society as this book comes to a close.
The society of Fahrenheit 451 is one that has been described as a corrupted dystopia across the course of the book. It is a society so caught up in its hedonistic, consumeristic lifestyle that it has lost sight of what is truly ennobling and worthwhile in living the human existence. The entire book follows Montag as he comes to realize the true value of books and the degree to which his own society has erred.
In a way, one might say that the "phoenix metaphor" applies on two separate levels: there's the potential recreation of society as a whole, ushered in through the atomic war which closes the book, but there's also Montag's own internal transformation, ushered in through his own encounters with death—both of Clarisse (his encounter with whom, along with her later disappearance, jump-starts his own crisis of faith with the society that surrounds him) and later the old woman, who burns herself alive with her books. From these experiences, the destroyer of books will be recreated as a protector of them, and his own journey in opposition to the State takes shape.
Thus, I would suggest that the central themes of the phoenix story are actually embedded deeply within the very structure of this book. Fahrenheit 451 is a story where death and redemption are closely intertwined (both for Montag as well as the entire society), and it is in recognition of those themes that Bradbury invokes the image of the phoenix directly towards the end of the book. The image of the Phoenix embodies that key thematic content which carries across the entire work.