What you are referring to takes place in chapter 12. Atticus leaves for two weeks, because there was an emergency session of the state legislature. The governor, according to Scout, wanted to do some work to help the poor. Here is the quote:
As if that were not enough, the state legislature was called into emergency session and Atticus left us for two weeks. The Governor was eager to scrape a few barnacles off the ship of state; there were sit-down strikes in Birmingham; bread lines in the cities grew longer, people in the country grew poorer. But these were events remote from the world of Jem and me.
The more important point about this development (Atticus leaving for two weeks) is that Calpurnia had to watch Scout and Jem. This allowed Jem and Scout to see Calpurnia's world. This is the chapter that they went to Calpurnia's church. They were able to see Tom Robinson's community. They also met Reverend Sykes, who plays an important role among the black community. Jem and Scout also experience things like "lining," the method that the black community uses to sing.
All of this opens their eyes. In this way, they are able to walk in another person's shoes for a while. This experience will also help them to have a context for the trial that they will witness.
Atticus Finch leaves for the state capital, Montgomery, for two weeks because there is an emergency session of the state legislature.
Added to the fact that Atticus will be gone for two weeks is the disappointing letter that Scout has received from Dill stating that he is not coming to Maycomb this summer because his mother has remarried and he now has a new father with whom he is purportedly going to build a boat. Now there will be
...no complicated plans to make Boo Radley emerge.... With him life was routine; without him, life was unbearable.
Perhaps the same could be said for the absence of Atticus. Certainly, Scout must feel pretty lonely without both Dill and her beloved father. But one morning she and Jem see news of Atticus as he is featured in a political cartoon in the Montgomery Advertiser. This cartoon satirizes the lawyer as "Maycomb's Finch" and reduces him to a boy wearing shorts and bare feet; also, he is chained to a desk. Frivolous girls call to him "Yoo-hoo!" as the servant of the state government continues his "diligent writing on a slate."
In what Scout calls his "newly developed...maddening air of wisdom," Jem explains to Scout that the cartoon is actually a compliment because it shows that Atticus is "doing things that wouldn't get done if nobody did 'em."
This remark hints at Atticus's character, which will be further demonstrated in the time leading up to and during the trial of Tom Robinson.