Atticus is worried about "ugly things" that the family will face i the next few months. Although we haven't read this part of the story yet, what sorts of things do you suppose have Atticus worried?
Atticus is able to shield his children from the ugly extremes of racism in Maycomb but, in taking this trial, he fears that Jem and Scout will see some upsetting things. The white population of Maycomb is generally racist against blacks. The sexual nature of Tom Robinson's trial is charged with a lot of public hatred and blatant bigotry: some of this will be directed towards Scout and Jem because Atticus is defending a black man. Atticus wants to prepare his kids for this.
