The mythical phoenix -- a bird that was consumed by fire at the end of its life, only to be reborn in the ashes -- is symbolic in three ways in Fahrenheit 451. The first ignores the rebirth aspect in favor of the fire: firemen wear phoenix symbols on their uniform, alongside the salamander, to show that they wield the power of fire and have authority over others. Their phoenix symbols are destructive.
The second is more literal; at the end, Granger tells Montag:
"...we've got one damn thing the Phoenix never had. We know the damn silly thing we just did. We know all the damn silly things we've done for a thousand years, and as long as we know that and always have it around where we can see it, some day we'll stop making the goddam funeral pyres and jumping into the middle of them."
(Bradbury, Fahrenheit 451, Google Books)
This statement shows Granger's willingness to face the mistakes of the past instead of hiding them; while society destroys itself because it is unwilling to remember the past, Granger and his followers want to show the past and take a different route. Their path will be the rebirth of civilization from the ashes of the old mistakes.
The third way is literal as well; Montag himself, once a destroyer with fire, is now going to be one of the people who gives society its second chance. He lived in fire for ten years, and now he is out of the fire and back into the real world.