As Montag is looking at Clarisse's face during their first encounter (7 pages in), he remembers a time when he was a small boy and there had been a power failure. So his mom found a single candle and they sat there "hoping that the power might not come on again too soon." Clarisse's face had a soft light emanating from it, so that was what reminded him of a candle flame, "not the hysterical light of electricity". That candle is a symbol of what is missing in their society; there is too much "hysterical light" and rushing, and Clarisse is different, so Montag is moved by it.
Fahrenheit 451 is set in the near future, a world where there is no real happiness anymore. Guy Montag is a fireman, who instead of putting out fires, sets them to books. In this reality, reading is a crime, and thinking for oneself is looked down upon. When Guy encounter Clarisse, he is struck by the life inside of her. Clarisse is a girl of seventeen, who enjoys nature and thinking outside of the box. When Guy walks Clarisse home, he is struck by a memory from his childhood.
But the strangely comfortable and rare and gently flattering light of the candle. One time, when he was a child, in a power-failure, his mother had found and lit a last candle and there had been a brief hour of rediscovery, of such illumination that space lost its vast dimensions and drew comfortably around them, and they, mother and son, alone, transformed, hoping that the power might not come on again too soon...
Clarisse is the one character who starts the transformation in Guy. She makes him begin to think about things in the past, and think about things for himself. Her young carefree spirit is appealing to Guy. He lives a life where everything he does is dictated to him, and he has to do it. His wife is a cold miserable woman. They spend any spare time constantly watching the wall sized TV sets, only to be "programmed" by what they watch. Clarisse opens Guy's eyes to the real world and makes him start his path of rediscovery of who he really is.