Atticus' statement, in To Kill a Mockingbird, "When its a white man's world against a black man's, the white man always wins" refers to one of the main themes which runs the entirety of the novel. Prejudice is a very important theme within the novel. The fact that Atticus (a white man) is defending a black man, Tom Robinson, has put the town in an uproar.
The statement Atticus makes refers to the fact that white men hold the power in the world. Atticus, regardless of his position defending Tom, understands this belief in Maycomb (and the rest of the South). Atticus is defining the fact that, no matter what, if it a black man against a white man, the white man will always win (regardless if the white man is at fault). For Atticus, this allows him to explain why the people of Maycomb are so against Tom Robinson. Even if Tom did not rape Mayella Ewell, the fact that the charges were made against Tom is enough for the people to find him guilty--simply based upon the color of his skin.
Atticus says this to Jem after Jem struggles to understand the guilty verdict in the Tom Robinson case, as the evidence clearly points to a verdict of not guilty. Atticus explains that while the twelve white men on the jury are, in his words, "reasonable," they did not exercise fairness in this case. They came to the guilty verdict because the case pitted the word of Bob Ewell, a white man, against that of Tom Robinson, a black man. Tom is clearly an honest man, while Bob isn't. However, when placed on the jury, the jurors defend the system of racist Southern justice at the time in which a white man's word always was regarded as truth when weighed against that of a black man. To regard a black man's word as more credible than that of a white man would undermine the entire Jim Crow system in which black people were regarded as inferior. This system played a large role in the verdict, and the color of Tom Robinson's skin was the deciding factor in his guilt. The men on the jury fall victim to their own prejudices; they are predisposed to see Tom as guilty, and thus they have trouble fairly evaluating the evidence against him.