This quote comes early in the book, when Montag first meets Clarisse. He is still in tune with the future society, although his subconscious is unhappy, and at first he doesn't connect with Clarisse because of her strange behavior and attitudes. At her age, Clarisse should be fully indoctrinated to society, but instead she acts for her own purposes, not for the purposes assigned to her.

"I'm seventeen and I'm crazy. My uncle says the two always go together. When people ask your age, he said, always say seventeen and insane. Isn't this a nice time of night to walk? I like to smell things and look at things, and sometimes stay up all night, walking, and watch the sun rise."
(Bradbury, Fahrenheit 451, Google Books)

As Beatty explains later, children in this society are indoctrinated and mentally controlled from an early age. They are taught not to think, but to do what they are told. They are slaves to their base emotions. They are confined to their assigned functions as gears in society, and have trouble thinking past these roles. Since Clarisse is able to think about the stranger aspects of society, such as the indifference to children killing each other for fun, she is considered "insane" by society, and takes the word as a badge of honor. Her family is unconventional and values human interaction, and it is possible that Clarisse's uncle intended the word "insane" to help camouflage her individualism from the government. In this future society, insanity is individual thought and action, and anything that does not directly benefit the government.

This quote comes from the very first chapter of this novel, when Montag meets Clarisse and it becomes clear that Clarisse is a young woman who definitely does not fit in to the culture around her. The quote in this question is one of the first things she says to Montag in order to introduce herself, and it points towards a very open attitude and character that is also slightly self-mocking. Note how this strangeness in her character is revealed a page or two on from this quote:

I rarely watch the parlor walls or go to races of Fun Parks. So I've a lot of time for crazy thoughts, I guess. Have you seen the two hundred-foot-long billboards in the country beyond town? Did you know that once billboards were only twenty feet long?

Clarisse is a character who is "seventeen" and "crazy" not just because of her age, but because of the way she questions everything about the culture around her, and constantly compares it to the past. Her decision to not partake of the major cultural entertainments of her day such as the new forms of media show that she is separate and different. The quote therefore serves to indicate what kind of character Clarisse is and to emphasise her difference in a world which seems to praise uniformity.