Atticus and Jem are discussing the Tom Robinson case in chapter 23, which involves juries, capital punishment, and the justice system in Alabama and in the United States. Atticus teaches Jem that he is not against rape being a crime worthy of capital punishment in Alabama, but he is against convicting someone of it based on incomplete and inaccurate evidence. He's also upset about Tom Robinson's conviction because it was based on prejudice and discrimination rather than truth. As a result, Atticus says the following:

"There's nothing more sickening to me than a low-grade white man who'll take advantage of a Negro's ignorance. Don't fool yourselves--it's all adding up and one of these days we're going to pay the bill for it. I hope it's not in you children's time" (221).

Atticus is saying that for hundreds of years in the South white men have taken advantage of black people and one day there will be a price to pay for it. The South already paid for slavery by fighting and losing The Civil War; it's only a matter of time before the South will pay again for the discrimination and prejudice used against blacks after that war. The year is 1935 when Atticus says this--less than thirty years before the Civil Rights movement of the 1960s. What he says is prophetic because the South is eventually forced to desegregate and play straight. Fortunately, there wasn't a second civil war, but many people lost their lives fighting for the Bob Ewells of the world to stop winning based on prejudice, and for African Americans to be treated fairly in court, in school, and in the voting booths. Atticus wants his son to know that the way things are at that point in 1935 won't be the way it is forever; and that one day the bubble will burst, but he hopes that it won't be so bad as to hurt his children in the end.

I like what the previous posters have said, but I'm not sure that it's necessary to see Atticus' statement in Harper Lee's novel To Kill a Mockingbird as prophetic -- or at least not anymore prophetic than it is responsive (on the part of the author) to the dramatic enactments of racial tension across the South and the border states in the 1950s, the decade before the publication of Lee's novel.

Any decent Civil Rights timeline (see, for example, the two PBS links given below) will show a number of significant events, including, for example, the Supreme court decision on Brown v. Board of Education, the Montgomery Bus Boycott, and the internationally covered lynching of Emmett Till.

At least one critic has written convincingly about the parallels between the Till trial and the Robinson trial in the novel; the critic doesn't attempt to show that the real trial entirely influenced the fictional trial, but he does demonstrate how the extreme media coverage of this lynching (or perhaps a more local, less publicized but parallel case) may have inspired the author. See Chura, Patrick. "Prolepsis and Anachronism: Emmett Till and the Historicity of To Kill a Mockingbird." Southern Literary Journal. (June 2000): 1-26.

The final link given here is a solid lesson plan on the historical contexts of Lee's novel.

To me, Atticus' language -- the metaphor of the growing debt, much like his talk of the "sin" of killing a mockingbird -- seems at least a little religious in nature (in a popular Christian sense). It echoes the idea of someone writing in each person's ledger and each person having to give a full accounting in the end, only it applies not to the individual but to the society as a whole ("we").

In Chapter 23 of To Kill a Mockingbird by Harper Lee, as Atticus and his son discuss the outcome of the trial of Tom Robinson, Jem mentions the injustice of the verdict based solely upon circumstantial evidence, his father tells him,

...The older you grow the more of it you'll see.  The one place where a man ought to get a square deal is in a courtroom, be he any color of the rainbow, but people have a way of carrying their resentments right into a jury box.

It is after this explanation that Atticus says "we're going to pay for it."  This statement reflects the Southern belief in the law of retribution: "What goes around, comes around," as the expression goes.  With his acute understanding of human nature, Atticus foresees the social revolution ahead in which civil rights will be enacted.  

Atticus says this after the trial of Tom Robinson has ended.  He and Jem and Scout are discussing the trial.  Jem says that it was not fair and Atticus responds with the quote you cite.

What Atticus is saying is that the black people will rise up one day because of the way they are being treated.  When he says "it" he means all the bad treatment of the black people.  He says it's going to pile up until one day the black people will make the whites pay for it.