Atticus Finch, as a character, is given development through some limited exposition of his background, through certain episodes that offer a glimpse into his fears, and through contrast with his sister, Aunt Alexandra.
Like most of the characters in the novel, Atticus Finch does not change over the course of the novel. He is, however, developed and deepened as a character. As we see the action of the story through Scout's eyes, we also see new information about Atticus Finch through the filter of his daughter.
One example of new information about Atticus comes when he has to shoot a rabid dog on the street. Scout and Jem had no idea that their father is or was the "best shot" in Maycomb. This fact helps to suggest that Atticus Finch is a man of great restraint and a deep sense of fairness.
Scout admires Atticus for his shooting talent, but Jem admires him for his gentlemanly restraint.
One particular episode in the novel offers an insight into Atticus' fears of losing his children. When they arrive in the midst of the mob outside of the jail, Atticus is uncharacteristically overwhelmed by the moment. He later articulates that his fear of losing them over presenting a bad example to them and losing their respect.
Finally, through contrast with his sister, Atticus shows his demeanor, his patience, and eventually shows the emotional strain of the trial.
Atticus has tried to be patient and understanding with his sister, but in this chapter he almost gives in to anger. He restrains himself, however, and Scout notices his feelings only as a subtle change in his behavior towards Alexandra, a “digging in.”
In these ways, Atticus Finch is developed as a character. The reader is given information about his past and made witness to events that both test and prove his character.