The last section of the book is called "Burning Bright." What is burned in the last section and in what way is it relevant to Montag's journey?

Much burning goes on in the last section of the novel, and all of it is relevant to Montag's journey, for all of it frees him to start a new life.
First, Montag drives with Beatty to a fireman call, only to find out the house to be burned is his own. Beatty sends him in to incinerate his home because it harbors illegal books. Second, Montag turns his fire hose on Beatty and burns him to a cinder. Finally, shortly after Montag flees his city, it goes up in the biggest fireball of all as a nuclear attack destroys it.
Montag is liberated from his home, which represented his unhappy life in his culture. Montag is also freed of an oppressive and bullying father figure who tried to impose orthodox thinking on him when Beatty dies. Finally, Montag and the other outsiders are freed to rebuild civilization on a firmer foundation once the city goes up in flames. They will preserve knowledge and use it as they band together to start over. Perhaps the most significant burning of all is the fire in a oil drum that the renegade readers gather it around. Montag marvels to see fire used not to destroy but to warm people and draw them into community.

In part 3, which is entitled "Burning Bright," Montag begins by burning his home and his book collection at Captain Beatty's command. Montag then burns Captain Beatty by shooting him with flames. After Montag flees the city, he meets up with Granger and a group of traveling intellectuals, who preserve knowledge by memorizing entire books in hopes of rebuilding a literate society once the dystopian nation is destroyed.
Towards the end of the story, the city is destroyed by an atomic bomb, which burns each structure to the ground. After the city is destroyed, the intellectuals sit around the fire and listen as Granger talks about a Phoenix, which is a mythical bird that builds a funeral pyre, burns itself, and rises from the ashes every few hundred years. The image of a Phoenix rising from the ashes corresponds to the title "Burning Bright." The title also corresponds to Montag completely burning his past and altering his life. Montag's new desire to pursue knowledge and rebuild a literate society also corresponds to the title of part 3.