At the beginning of the novel Scout tells us about the Finch family history. Why is this?

In my opinion, the reason for this is to give us a good idea as to how the Finch family fits in with the rest of the society in Maycomb.

As we see later in the book, the structure of the society in Maycomb is very important.  Various kinds of people are expected to take on very different roles in the society.  People like the Ewells are expected to be the scum of the society, people like the Finches are expected to be the cream (sort of how Aunt Alexandra acts).

By telling us who the Finches are, the author gives us a sense of where they fit in.  At the same time, she gives us an understanding of how Atticus is something of a rebel because he does not take his expected role in society -- he doesn't act like part of the elite.