What do the characters in Fahrenheit 451 represent?
Each of the five main characters represent a type of reaction to the collectivist government that controls all its citizens.
Montag's wife, Mildred, represents the unthinking acceptance of control; she has no desire to be anything more than she is each day, and cares about nothing except for her television programs, which lack intellectual content.
Clarisse represents the freedom of the past. She is critical of society and looks beyond the surface to see the misery underneath the patina of comfort. She speaks with Montag, triggering his latent individualism, and is a danger to the government; it is likely that they have her killed to prevent her from spreading seditious thoughts.
Chief Beatty represents the knowing continuation of the governmental system. He knows what mankind has lost, their freedoms and individuality, and he genuinely thinks that this is a superior future to live in. He believes strongly in his mission, has read extensively to support his ideals, and dies to defend them.
Faber represents the unwilling acceptance of the government; he was against their directives, but said nothing and did nothing, and by the time he felt ready to act it was too late. He is scared of change, and scared of being caught reading, so he is only pushed to action when Montag confronts him.
Montag represents the passage from pawn to individual. At first, he has no idea that things were ever different, but something inside him is dissatisfied, and he begins to steal books. As the book progresses, his waking mind questions the superficial nature of people and things around himself, especially the pointless television programs. It is the full individual, Clarisse, who opens his mind, and he feels a connection to her even after her death:
He walked on the track.
And he was surprised to learn how certain he suddenly was of a single fact he could not prove.
Once, long ago, Clarisse had walked here, where he was walking now.
(Bradbury, Fahrenheit 451, Google Books)