"The Hearth and the Salamander" contains two important motifs that recur in Fahrenheit 451. A "hearth" is the stone structure that contains a fireplace, and was considered the center of a home during the pre-electrical age. Since the first section of the novel focuses on how Montag reconciles his home life with his work, the hearth represents his home.
In legend, salamanders were arcane creatures that could live in fire, put fires out, and poison people and land. While none of this is true, the imagery of a salamander in fire has persisted to this day, and it is used both as a symbol for the firemen, and as the name of their "firetrucks," which set fires instead of extinguishing them. Using the two symbols together -- the common image of a "warm hearth" contrasted with the Montag's cold and sterile home -- draws attention to his growing unease and dissatisfaction.
Bradbury named this section "The Hearth and the Salamander" because it foreshadows the conflicts which will occur later in the novel. A hearth, for example, is the name given to the floor of a fireplace and this alludes to Montag's domestic life, especially his marriage to Mildred. Similarly, the salamander, a lizard-like amphibian capable of withstanding fire, alludes to Montag's job as a fireman.
As the novel opens, Montag seems content and fulfilled with both his marriage and his career. But as the story progresses, the reader quickly realises that Montag is, in fact, deeply miserable in both of these areas. His marriage to Mildred, for instance, is loveless and empty. His commitment to being a fireman is also tested when he meets a woman who sacrifices her life by choosing to be burned with her books. By using this title, then, Bradbury alludes to Montag's unhappiness and paves the way for his rebellion.