This is the time of the Jim Crow laws in the South. Everything was segregated, including the court house. The Black community all must sit together in the balcony, while the White community sits down below. They also must wait for the Whites to enter the court house before they go up the stairs (as seen in ch. 16). According to Scout's description "The Colored balcony ran along three walls of the courtroom like a second-story veranda, and from it (a person) could see everything" (166).
Ironically, since the children are late in entering the court house and find there are no more seats downstairs, they end up sitting in the Colored balcony after Reverend Sykes makes a place for them. He "steered (them) gently through the black people in the balcony. Four negroes rose and gave (them) their seats" (166). The children sit there and watch the trial, stay there to wait for the verdict, and stand up along with the rest of the Black community to honor their father as he later passes by as he exits the court room.
Symbolically, this separate seating in the court house shows the segregation that permeates Maycomb, a place where schools and other public facilities are segregated, where Blacks are seen as inferior and undeserving of employment other than menial labor, and where they are treated as second class citizens.
Also symbolically, it shows how the Finch family is willing to step beyond the rules of segregation and treat the Black community as their equals, deserving of respect, fairness, and justice. Atticus does this in his defense of Tom Robinson, and the children do it here as they sit with Tom's family and friends in the Colored balcony. It is only in ch. 21, when Calpurnia enters with a note for Atticus to let him know the children are missing, that Mr. Underwood points out where they are sitting. And Atticus, after some discussion, lets them remain there to hear the verdict.