Why are these quotes important in the book To Kill a Mockingbird? "You ain't got no business bringin' white chillun here—they got their church,...

Both questions speak to the racial divide present in Maycomb at the time of the Tom Robinson trial.

In the first, Calpurnia brings Jem and Scout to her African American church.  In this quote, we see that the racial divide cuts both ways, and that, to some extent, the Black churchgoers appreciate having an all-Black church in order to have their own space in society.  That Calpurnia has brought two white children into that church...

Both questions speak to the racial divide present in Maycomb at the time of the Tom Robinson trial.

In the first, Calpurnia brings Jem and Scout to her African American church.  In this quote, we see that the racial divide cuts both ways, and that, to some extent, the Black churchgoers appreciate having an all-Black church in order to have their own space in society.  That Calpurnia has brought two white children into that church is upsetting to this congregant.  Yet, in the way he asks Cal, rather than telling her (...ain't it, Miss Cal?), we see that the congregant still respects Cal as a leader within the church.

The second quote is spoken by Bob Ewell as part of his testimony against Tom Robinson.  In his use of the "n" word in a formal court, we see that language usage was quite different at the time.  One cannot imagine using such a word while under oath these days.  His use of the colloquialism "ruttin'" also shows Bob to be uneducated, as those properly educated would likely have used different terminology.