What is the significance of the scene in which Montag first meets Clarisse?

In my opinion, the significance of this scene is that it
represents the start of Montag's transformation in this book.  After meeting Clarisse,
Montag starts to think and starts to reconsider his opinions about the society in which
he lives.

When he meets Clarisse, Montag still thinks of
kerosene as perfume.  This symbolizes (to me) that he totally buys in to the ideas of
his society.  He thinks that the smell of the stuff that is used to burn books is
great.

But as he talks to Clarisse, he starts to have to
think.  She is just too different from other people in his society.  By the time they
are done talking, he has thought about a tender moment with his mother and he has
started to have to consider whether he is happy.

In other
words, he has gone from being a contented member of society to being confused -- he has
had to start to think about things like his emotions, things that have no place in his
society.