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...

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.