Scout's fight with her Cousin Francis is not one of the significant events in the novel--aside from it proving that she has a strong left-handed punch--but it does serve several purposes. It is the last time that Scout uses her fists in anger (though she does land a strategic kick to the groin to one of the men in the lynch mob the following summer). It teaches her Uncle Jack to make sure he learns all of the facts before dealing out punishment; and it serves to show that Jack is a man of his word, since he honors Scout's request to refrain from telling Atticus about the insults Francis has made.
Uncle Jack was a prince of a fellow for not letting me down. (Chapter 9)
It also allows Scout, who believes she is hidden from view, to listen in on Atticus's and Jack's conversation in which Atticus deliberately lets her hear their talk about the trial, and how he hopes
"... that Jem and Scout come to me for their answers instead of listening to the town. I hope they trust me enough..." (Chapter 9)
Scout also learns a lesson in how Atticus has an uncanny ability to discover many of his children's secrets.
... I never figured out how Atticus knew I was listening, and it was not until many years later that I realized he wanted me to hear every word he said. (Chapter 9)