In "Fahrenheit 451," fire symbolizes both mindless and brutal destruction, and also an opportunity to cleanse and rebuild, to start over again.
In Montag's society, they use fire as the main force of destruction, not only of books, but of independent thinking and rebellion. Yes, they burn books, but in doing so, they use fire to snuff out and destroy people's ability to use books to help them to think on their own. As Beatty puts it,
"If you don't want a man unhappy politically, don't give him two sides to a question to worry him."
Books present two sides of the story, the good and bad in life, and encourage people to think on their own. And it's not only books in houses that they burn, they take away anyone who is slightly different or who might be causing unrest, like Clarisse's family. People are so afraid of their houses being burnt that the threat alone keeps them from reading and thinking, and expressing discontent--this is what happened to Faber. He said that he had been a "coward" all these years. Houses are burnt, and so are free-thinkers and any dissenters.
The second symbolic meaning behind fire is that of rebirth, rejuvenation, and second chances. This is best expressed in the myth of the Phoenix, that Granger describes at the end of the book. A bird would burn himself up in a fire every few hundred years, and
"every time he burnt himself up he sprang out of the ashes, he got himself born all over again."
So, Granger says, that is what happening to their society. It is burned to the ground through fire, the war, but they have a chance to be reborn--to start over and not make the same mistakes. Sure, Montag's house was burned to the ground and destroyed, but that provided him the opportunity he needed to leave his past behind and start again, the right way. Sure, their city was destroyed by fire, but, it gave the right people the chance to rebuild, in the right way.
So, fire destroys, but it also provides opportunity for rebirth, for starting over, and for building things that are devoid of the mistakes that destroyed things in the first place. I hope that those thoughts helped a bit; good luck!