What is the role of the character Clarisse, and why is she important to the narrative of Fahrenheit 451?

Clarisse McClellan is an anachronism in the world of Fahrenheit 451; she becomes a reminder to Montag of what has been lost. Furthermore, she becomes an agent of change for the fireman. 
In Part One, when Montag turns the corner and meets the girl

...who seems to have a kind of gentle hunger that touched over everything with tireless curiosity,

he is subtly reminded of what is missing in his life. Unlike his desensitized wife, Clarisse possesses eyes that are dark and "shining and alive." In fact, these eyes cause Montag to feel that he has said something "quite wonderful" to her. Then, Montag even sees himself in her eyes in a "brief hour of rediscovery."Clarisse asks Montag probing questions such as if he has ever read any of the books that he burns and if he ever stops to think about what she asks him before answering. Further, she informs Montag of things that he has never noticed or talked about.
After Clarisse departs, Montag reflects upon what this girl has asked him. Then, he realizes,

He wore his happiness like a mask and the girl had run off across the lawn with the mask and there was no way of going to knock on her door and ask for it back.

Therefore, it is with different eyes that Montag looks around his house now, as Clarisse has awakened some deadened feelings in him.