What did Scout and Jem learn about segregation and the inequalities between blacks and whites in To Kill a Mockingbird?

From their experiences at Calpurnia's church and from their own observations at the Tom Robinson trial, Jem and Scout discovered first-hand the differences between the two worlds of the white man and black man. They were already aware of the segregated living conditions, but they apparently had little contact with Negroes other than with their housekeeper, Calpurnia. When she decides to take them to her church, they are ready and willing to see a different side of Maycomb. Although they are hassled by Lula as they enter the church and are aware of stares from the congregation, they nevertheless are made to feel at home. They witness the poor conditions of the church, the lack of hymnals (and literate people to read them), and the repeated passing of the collection plate in order to gain donations for the Robinson family.

At the trial, Jem and Scout sit in the separate Negro section with Reverend Sykes. They here Tom referred to as "nigger" by both witnesses and the prosecutor. They carefully examine the evidence presented by Atticus and determine that Tom Robinson could not have harmed Mayella--but that Bob Ewell likely did. It seems obvious to both children that the jury (though all white) will find Tom innocent of the charges. When the guilty verdict is delivered, they are both aware that the color barrier is the reason. As Atticus had previously hinted, no all-white jury in Alabama can be expected to take the word of a black man over that of a white man--even if the white man is Bob Ewell.