What is the function of relating the Finch family history at the outset of the novel?

The main reason to give some background on the Finch family is to introduce them as a well-established and important family in the history of Maycomb.  The most famous ancestor, Simon Finch, came to Maycomb from England and settled in an area later known as Finch Landing.  There Simon Finch trapped animals and practiced medicine.  Simon Finch was also a slave owner.  After gaining some wealth, the family lost all of its money during the Civil War. 

Because they are an old Southern family, they are well-respected in the community.  They are also considered a higher class of people because of Atticus’ law degree and tenure in state politics.  In the South, family heritage is important and a basis for social class. 

Atticus also represents a new generation of Finches.  Although his ancestor, Simon Finch, owned slaves, Atticus fights for the rights of Tom Robinson, a black man.  He truly shows the evolution of values and beliefs in the South. 

Introducing this family history gives the reader a solid background on where the members of the Finch family began and how they have developed since then.