Clarisse is the teenage neighbor Montag meets when he is beginning to question the structure of the society around him. She befriends him, and seems to be motivated by nothing more than a human desire for friendship and companionship. She makes it clear that her family likes to spend time together, simply talking, and she may assume that it's natural for others to do so as well. She really is an innocent character, so I doubt there's any ulterior motive to her relationship with Montag. She does ask him to consider his own happiness, and his place in the society, but this seems to be more about her actually being interested in him as a human being.
This is certainly not something common in the world of the novel. Montag's relationship with his wife isn't even as close as his relationship with Clarisse...especially when it comes to knowing about the happiness and interests of the other person. I really see Clarisse as a lonely girl who, seeing someone clearly unhappy (Montag), attempts to brighten his day and bring some human interaction into his life.