In chapter 16 of To Kill a Mockingbird, what news about Atticus defending Tom Robinson does Scout overhear?

Having spent a tense night before the trial by standing up to the angry mob, Atticus makes his way to the courthouse.  Outside this courthouse, Scout overhears the old men in khaki pants and white shirts with suspenders talking,"resentful of the interruption of their comfortable routine."

Scout overhears one say that the court appointed Atticus Finch to defend Tom Robinson.

'Yeah, but Atticus aims to defend him.  That's what I don't like about it.'

Scout reacts  to this news by saying that it puts a different light on things.  Atticus could have used this as an excuse. But, she is baffleded by the town's being upset with him and having come as a mob last evening:

He had to, that's why he was doing it, equaled fewer fights and less fussing.  But did that explain the town's attitude?  The court appointed Atticus to defend him.  Atticus aimed to defend him.  That's what they didn't like about it.  It was confusing.

While this news is confusing to Scout, it is not to the reader.  For the conventional wisdom is that Tom Robinson should be convicted because he is a black man who interfered in the lives of white people.  He simply had no business on the Ewell property. Period.

What news does Atticus bring about Tom Robinson in "To Kill a Mockingbird"?

In Chapter 24, Atticus interrupts Aunt Alexandra's missionary circle to ask Calpurnia if she could take him to see Helen Robinson. Atticus proceeds to tell Cal, Alexandra, Miss Maudie, and Scout that Tom has been shot dead. Atticus explains that during the inmates' exercise period, Tom charged towards the fence and began climbing it. After being instructed to stop, the prison guards fired a few warning shots before they aimed at Tom. The prison guards ended up shooting Tom Robinson seventeen times, killing him during his escape. The women are visibly shaken after hearing about Tom's tragic end, and Atticus tells them that he thinks Tom was sick of "white men's chances." Despite having the opportunity to appeal the ruling, Tom decided to take matters into his own hands by attempting to escape. Unfortunately, Tom Robinson was shot multiple times by the prison guards and died while he was attempting to escape. 

What news does Atticus bring about Tom Robinson in "To Kill a Mockingbird"?

I assume you are referring to Chapter 24, when Atticus comes to tell the family that Tom was shot while trying to escape from prison.  Always trying to understand another's perspective, Atticus explains that Tom lacks any hope for an appeal after having been convicted by a jury that could not have believed he was really guilty. 

In Harper Lee's To Kill a Mockingbird, what news does Atticus bring home about Tom Robinson?

There are many times that Scout records the events of her father returning home from work. The one time that has anything to do seriously with Tom Robinson is when Atticus has news of Tom's death. Scout was attending one of Aunt Alexandra's tea parties when she heard the front door slam and heard Atticus come in. She checked the time and realized that it was too early for him to be done with the day's work. She also remembered that Atticus usually stayed away from the house longer on the days that the Missionary Society met with Aunt Alexandra at the house. Atticus came home to ask Calpurnia to accompany him to Helen Robinson's house to tell her the sad news. Atticus explains as follows:

"They shot him...He was running. It was during their exercise period. They said he just broke into a blind raving charge at the fence and started climbing over. Right in front of them--" (235).

Atticus had hoped to appeal the decision of the court on Tom's behalf. He had told Tom not to give up hope because they would continue to fight for his freedom through the justice system. Sadly, Atticus surmises,

"I guess Tom was tired of white men's chances and preferred to take his own" (235-236).

The news is obviously sad for the people who supported Tom. Any hope for Tom to get his appeal and return home to his family is completely over at this point.