Atticus's primary character motivation is to protect and defend innocent people like Tom Robinson. Atticus is also motivated to ameliorate racial injustice and inequality in his prejudiced town of Maycomb by setting precedence during Tom Robinson's trial. In addition to protecting Tom Robinson from racist community members, Atticus is also motivated to raise his children to be morally-upright, tolerant citizens. One of Atticus's biggest fears is that the prevalent racism will rub off on Jem and Scout and negatively influence them, making them become prejudiced, hateful individuals.
Aunt Alexandra is motivated to positively influence Scout into behaving like a proper Southern Belle. Alexandra is opposed to Scout's tomboy personality and cannot stand the fact that she wears overalls. Alexandra tries her best to expose Scout to social functions and encourages her to dress like a lady. Aunt Alexandra is also motivated to teach her niece and nephew about their respected family heritage.
Boo Radley's primary motivation to develop a friendship with Jem and Scout. Boo attempts to communicate with the Finch children by leaving them small gifts in the knothole of his tree and demonstrates his compassion by covering Scout's shoulders on the night of Maudie's house-fire and protecting the children during Bob Ewell's vicious attack.
Judge Taylor is motivated to set a precedence of justice and racial equality in his court by specifically appointing Atticus Finch to defend Tom Robinson. Instead of having the inexperienced Maxwell Green take the case, he has Atticus defend Tom Robinson because he knows that Tom is innocent. Judge Taylor is aware that Atticus will valiantly defend Tom and possibly sway the jury's decision, which is why he appoints Atticus to the case.
In Harper Lee's To Kill a Mockingbird, character motivations drive the plot.
Atticus' motivations, which drive his actions, are based on being a man of honor. He is not racially prejudiced, and so he is willing to defend Tom Robinson as he would any many with a right to a fair trial. Atticus also is consistent: his sense of honor and integrity is something that drives him not only as a man and a citizen of Maycomb, but as the father he wants to be to his children in order to bring them up to be responsible, compassionate people.
Boo Radley is intrigued by the children. I believe he is motivated to want to be with them because they are interested in him, and they make him laugh. We see this when the kids are playing the "tire game" and Scout's tire rams into the side of Boo's house. Although it frightens her, she later admits to hearing a laugh outside. His fondness for the children and interest in their lives ultimately save them from Ewell's attempt to murder them.
Lastly, Bob Ewell is motivated by ignorance and hatred. He refuses to live with what he perceives as shame for his daughter's physical advances toward Tom Robinson, so he accuses Tom of rape. He is motivated by a sense of superiority in how he acts towards Tom and other blacks. And his verbal attack of Atticus on the street (when he spits on him), and ultimately his attack of Scout and Jem, are motivated by his deep hatred for those who do not support his malicious nature/ideas. He is the face of evil in the novel.
To best understand a character, it is important to understand what motivates him or her.