What fact about Atticus' defense does Scout learn from the Idlers' Club?
When the children first enter the courthouse, Scout gets separated from Jem and Dill and stands by the stairwell to wait for them. Scout finds herself in the middle of the Iders' Club, which consists of old men who listened to every case as "attentive critics of courthouse business." Scout overhears their conversation and listens as one of the men comments that the court appointed Atticus to defend Tom Robinson. Scout is shocked to learn that her father had to defend Tom whether he wanted to or not, but Atticus never mentioned it to her. Scout finds it odd that Atticus would not tell them that information because it would have given them an excuse when they were defending their father on the playground and in school. Scout goes on to mention that even though Atticus was appointed to defend Tom, the town did not want Atticus to argue his case and essentially let the prosecution win. Atticus is not concerned about the town's feelings, and defends Tom Robinson to the best of his ability.
What Scout learns is not really so much about the defense itself. Instead, she learns from the Idlers' Club something about why Atticus is defending Tom Robinson. This can be found in Chapter 16.
Ever since it has become known that Atticus will defend Tom Robinson, Scout and Jem have been hearing people criticizing their father. Many whites are upset that he would be defending a black man accused of raping a white woman.
When Scout is listening to the Idlers' Club, she hears that Atticus was appointed to defend Robinson. She wishes she had known this because then she could have defended herself and her father by saying he was not doing it by choice.
This is important because it shows us something about Atticus. It shows us that he does not want to defend himself as if he is doing something wrong. He wants to defend Robinson regardless of what others think.