When Clarisse stops walking Montag to the subway, he is at first unsure why he feels strange. He thinks of the streets as empty without her presence, but can't quite put his feelings into words. When his wife tells him that she thinks she heard that Clarisse was run over by a car, Montag is so shocked that he develops a fever. When trying to work through his feelings, he has this epiphany:
"It's not just the woman that died," said Montag. "Last night I thought about all the kerosene I've used in the past ten years. And I thought about books. And for the first time I realized that a man was behind each one of the books."
(Bradbury, Fahrenheit 451, Google Books)
In his mind, since Clarisse was so different from normal people, he relates her death to his own burning of books. Just as her human life was unique, each book is the unique product of a deliberate creative process; the people who wrote the books live through them after their deaths. Clarisse didn't write a book, and her life was so meaningless to others that Montag's wife simply forgot to mention it; Montag realizes that Clarisse will live on only through his memories.
In Fahrenheit 451, the news that Clarisse has died affects Montag in two ways. The first of these is physical: the day after Mildred breaks the news to him, for instance, Montag develops "chills and fever." Mildred notes that this is the first time that Montag has ever been "sick," which indicates the significance of this event for him.
Secondly, Clarisse's death also has an emotional effect on Montag. He does not go to work the next day, for example, and talks to Mildred about the woman he burned the previous night. He suggests quitting his job for a while and starts to wonder if books really do contain an important message.
For Montag, then, Clarisse's death creates a turning point in his life, one which makes him realise the emptiness of his existence and the need for change:
"We need not to be let alone. We need to be really bothered once in a while."