Scout, in her mature naivete, states what it means quite succinctly:
In Maycomb, grown men stood outside in the front yard for only two reasons: death and politics. I wondered who had died. Jem and I went to the front door, but Atticus called, "Go back in the house."
The reflects the kind of small-town mentality exhibited throughout the story. Men only call you out into your yard to relay the news of a death, or to express support or disapproval for political candidates and causes. Scout doesn't understand the true nature of the mob appearing (although she will later in the chapter), so she asks "who had died." Atticus clearly does understand, as he orders his children back into the house.
Aunt Alexandra does not directly state her thoughts on Tom's innocence of guilt, but she does express her ideas about Atticus defending him. Scout relates that she heard the end of a conversation between Atticus and Aunt Alexandra, in which Atticus tells her that he's:
". . . in favor of Southern womanhood as much as anybody, but not for preserving polite fiction at the expense of human life," a pronouncement that made me suspect they had been fussing again.
I sought Jem and found him in his room, on the bed deep in thought. "Have they been at it?" I asked.
"Sort of. She won't let him alone about Tom Robinson. She almost said Atticus was disgracin' the family Scout.
Thus, it doesn't really matter to Aunt Alexandra whether or not Tom is innocent, or whether or not he gets a fair trial. All she cares about, as she proves time & time again, is the family name. To her, Atticus' defense of a black man is akin to disgrace for an old, established family like the Finches. Of course, she may truly think Tom deserves a fair trial, but she doesn't want her brother to be the one to ensure he gets it.