Give an example of dialogue between Atticus and Aunt Alexandra that advances the plot in To Kill a Mockingbird.
One of the most distinct purposes of the character of Aunt Alexandra in the story is to fill in some of the gaps of societal nuances of the setting of the story. Much of the natural sense of prejudice and segregation present in such a town of that era is left out of the story because Atticus (and therefore Scout) leaves the subject largely unaddressed. This includes both racial segregation as well as social class segregation (social separation of the professionals, the working poor, and the poor white "trash"). Atticus is a rare character in his ability to treat everyone equally. Scout, as a narrator, is therefore biased by ignorance, innocence, and the influence of her father.
When Aunt Alexandria arrives at the house in chapter 13, she immediately invokes a feminine presence that was void until this point. She mentions to Atticus in chapter 14:
You've got to face it sooner or later and it might as well be tonight. We don't need her now (137).
Alexandria is speaking of Calpurnia. As this very high profile and racial case advances for Atticus, Alexandria believes it both unwise and innappropriate to have a black housekeeper standing in as the children's only maternal influence.
Later in the story, Alexandria gives her opinion of the "mob" scene at the jail. Scout is surprised by Walter Cunningham's presence with the rest of the mob and threatens to hurt Walter (Junior) at school as a result. When chastized by Atticus about this idea, Alexandria interrupts with:
You see don't you...what comes of things like this. Don't say I haven't told you (158).
Alexandria's presense in the house and in the story furthers the plot by introducing the common societal attitudes pertaining to the setting of this story. Such attitudes had previously gone mostly neglected because the main adult characters (Atticus and Miss Maudie) have an unusual sense of integritity and are almost above this societal norm. As a result, the main children characters have been kept blissfully unaware that these attitudes even exist. Aunt Alexandria is the key character used as a turning point for Scout's growth and maturity in the story.