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.