In Harper Lee's To Kill a Mockingbird, Scout (and Jem) are greatly accustomed to the workings of the court system, and have a sophisticated understanding of their father's profession and the interactions between the members of the court.
Scout understands what her father does for a living, but sometimes it is hard for her to withstand the criticisms he receives for the cases he takes (like Tom Robinson's), especially when she has to hear about it from friends and relatives.
Inadvertently, Scout's father has raised his children listening to both sides of an argument before passing judgment. Without a wife, Atticus relies on his sense of fair play and the ability to place himself "in someone else's skin" in order to better understand others, which mirrors his behavior in court.
This sense of the rules of court comes into play when Scout gets into trouble with Uncle Jack over her fight with her cousin Francis. Uncle Jack immediately punishes Scout without hearing both sides of the argument. Scout draws his attention to this:
...you never stopped to gimme a chance to tell you my side of it—you just lit right into me. When Jem an' I fuss Atticus doesn't ever just listen to Jem's side of it, he hears mine too...
Atticus runs his home with many of the same rules exhibited in the courtroom, and Scout understands the equity of this, in that both sides are permitted to have a say.
It is not just that Atticus is a lawyer that affects Scout's mindset and behavior: it is seeing his role as a fair-minded, dedicated, ethical man that affects Scout. She trusts him implicitly, and Atticus is very careful to make sure that trust is not broken, more for his children's faith in him than for any other reason.
Scout knows her father is a lawyer, but what most influences her is his abiding dedication to providing his best legal counsel, regardless of the economic or racial issues. His sense of equality and dedication, which are a part of her father first, before his profession, greatly influence Scout.