The case is quite simple. Atticus adds that it is as simple as "black and white." This statement calls attention to its simplicity and it also illustrates that race has had a significant role in the case even coming to trial. Atticus has a small hope that the jury will realize how racist thinking has affected the case.
Atticus says he has sympathy for Mayella but her poor situation in life does not justify her putting Tom's life/fate in danger. Still, Atticus explains to the jury why Mayella shifted the guilt to Tom: because of their (the jury's and the South's) racist thinking. Since Mayella broke the "code"—reached out, sexually, to an African-American and got caught—she felt she had no choice but to push the guilt onto him. Atticus means that what she did is wrong, but the racist code is what drove her to it.
Atticus then uses the logical evidence that Mayella was beaten by someone who led with their left hand (ruling Tom out).
Again, Atticus gives the reasons why Mayella and Bob accused Tom of this crime:
We do know in part what Mr. Ewell did: he did what any God-fearing, persevering, respectable white man would do under the circumstances—he swore out a warrant, no doubt signing it with his left hand, and Tom Robinson now sits before you, having taken the oath with the only good hand he possesses—his right hand.
Atticus is basically saying that what they did was wrong, but they did it because of the code barring whites from associating with blacks. He is saying what they did was wrong but you (the jury) will understand why, and this racist justification has no place in a court of law.
Atticus calls out the racist beliefs that many have—"that all Negroes lie, that all Negroes are basically immoral beings . . ." in order to stress the fact that the only reason Tom is a defendant is because of such thinking. Atticus continues saying that all men are equal in law, in the court; thus, he implores the jury to treat Tom as an equal, to look past their own possible prejudices. Atticus quotes Thomas Jefferson to make this point. He concludes by saying they (the jury) are the court and invokes God as he asks that that they do their duty.
Atticus notes that racism is what caused Mayella and Bob to accuse Tom. Racism is what the jury must overcome in order to free Tom. And in doing so, Atticus calls attention to racism overall, not just in the jury.