Atticus confides to his brother Jack that he worries about how Scout will handle what she hears during the next several months.What is she likely to hear?
Uncle Jack comes to visit during Christmas in chapter 9. The turn of the New Year will bring with it much talk of the upcoming trial. What Atticus is referring to here is the gossip in Maycomb of the details of the trial. Considering it is a case of a white man versus a black man, likely Atticus is aware of the racial and prejudiced charge that will hang in the air. Also, because the case involves the Ewells (who are considered "trash" by all respectable citizens of the county) it is likely that conversations will include details which would be inappropriate for children (and at that time, ladies).
Atticus is likely aware that not only will Bob Ewell himself be stirring up trouble, but as people begin to pick sides, the truth of the situation will be skewed and some of the worst sides of people will come out.
Keep in mind that Atticus Finch has not lived to shelter nor protect his children from such attitudes. Rather, he teaches them to view everything from an educated perspective. He likes to be the filter for such lessons because he knows his children need to hear things in black and white and be taught how to make decisions with respect and integrity. There will be plenty of "lessons" spoken in the next several months, but coming from the mouths of close-minded people who will refuse to present things from objective angles. Atticus knows his own name will come up in many of these conversations, and that his children are very impressionable. He rightfully worries that their heads will be filled with all kinds of thoughts and ideas, and they will be too young and too inexperienced to sort them all out properly.