The Phoenix is, in the mythology of the Greeks, Romans, Arabians (and others), a bird which is either immortal or sustains itself throughout history. The Phoenix would live 500 to 1000 years, ignite itself and be reborn/remade from the ashes. There is a lot of symbolism between the phoenix and Fahrenheit 451.The society Montag runs from had based the control of citizens on burning literature. Thus, future generations of illiterate, thoughtless citizens were reborn amidst the ashes of burnt books and dissidents.
Granger tells Montag, "... we've got one thing the Phoenix never did. We know the silly thing we just did" (146). Knowing literature and history is necessary to avoid repeating the same mistakes. When Montag's mind is opened to other ideas via literature, he also wants to consider alternative ways of living and knowing. Montag's rebirth is more profound because he knows the limitations of his old life and the possibilities of his new life. He doesn't want to be thoughtlessly reborn as the obedient fireman. He wants to be reborn into a free thinking individual, aware of the dangers of oppression and open to new ideas.
The state Montag had lived in, prior to meeting Granger, sustained control by erasing history. No one would know how things used to, or could, be. With historical and literary knowledge and awareness, Montag, Granger, and the other book people would remake/remember themselves and their history, born anew out of the ashes of the city behind them.