Jem thinks that the jury was very quick to convict Tom Robinson, but Atticus says that isn't so. He says:

That jury took a few hours. An inevitable verdict, maybe, but usually it takes ‘em just a few minutes.

Atticus reveals that the long time jury took was due to Mr. Cunningham:

"This time—” he broke off and looked at us. “You might like to know that there was one fellow who took considerable wearing down— in the beginning he was rarin’ for an outright acquittal.”

... “One of the Cunninghams?” Jem yelped. “One of—I didn’t recognize any of ‘em... you’re jokin’.” He looked at Atticus from the corners of his eyes.

Jem is surprised at this news, but we might not be. Throughout the novel, the Cunninghams are set up as a contrast to the Ewells. Both families are poor, but while the Ewells are white-trash poor, the kind of people who take handouts and let their homes fall into wrack and ruin, the Cunninghams are the worthy poor. They have no money, but they try honorably to pay their debts, even if it is with only a sack of potatoes, and they never take a handout, as Scout tries to explain to her first-grade teacher.

This kind of honor, Harper Lee implies, extends to how they serve on a jury. Mr. Cunningham, unlike most of his white neighbors, isn't trying to hold the Black people down because he'll benefit from doing so. The Cunninghams are the kind of honorable people who do the right thing even when it hurts them.

Of course, in this case, the Cunningham in question goes along with the guilty verdict, but Atticus nevertheless sees progress in the way he delayed the rush to injustice. It was a small but significant gesture.

Atticus explains to the children that the jury took a while to deliberate because there was one juror who did not agree with the others. In such a case, the jury must continue to discuss the evidence until everyone is in agreement on a verdict. Atticus reveals that the jury debated for two hours instead of the usual few minutes due to the doubts of a Cunningham.

This piece of news is quite shocking to Jem and Scout, but Atticus does not seem very surprised. He explains that the Cunninghams are loyal to people whom they respect. He believes they found a new respect for the Finch family after the night outside the jail when Atticus did not back down from the angry mob and Scout charmed the group into peace.

In addition, Atticus explains, he had the opportunity as defense attorney to not accept this juror, but he kept him “on a hunch.” His feeling was correct because this was the only juror who held out. From his explanation, it seems the juror held out as a sign of loyalty to Atticus, but hopefully it was also to seek truth.

Atticus recognizes the importance of the verdict, even though it was not a just one. He says, “That was the one thing that made me think, well, this may be the shadow of a beginning.” He is alluding to a future of better justice and fairness for society. During the trial, Atticus had clearly proved that Tom was innocent. In a fair court, in an equal society, in an enlightened community, Tom would have been acquitted immediately; in fact, the case most likely would have been thrown out of court early on in the proceedings. However, this community represents a time period of ignorance, bigotry, unfairness, and prejudice. As a result, because Tom is black, people automatically assume his guilt, even in the face of evidence to the contrary. Therefore, since the jury actually discussed the case for two hours is a positive sign that people are beginning to open up their hearts and minds.

Atticus is hopeful for the community’s progress. In his words, “Serving on a jury forces a man to make up his mind and declare himself about something.” Although Atticus believes people are wary to stand up, and he realizes that it was an inevitable verdict, he sees a message in this jury’s actions.

Atticus tells Scout and Jem that the jury took longer than he expected to come to a verdict because "there was one fellow who took considerable wearing down - in the beginning he was rarin' for an outright acquittal".  To the children's surprise, that fellow was a relation of the Cunninghams.

Atticus says that the verdict was inevitable, and that usually, it would have taken the jury "just a few minutes" to convict Tom Robinson.  This time, however, because of the one holdout, it took "a few hours".  Atticus is heartened by this fact; he thinks that "this may be the shadow of a beginning" of change in attitudes and social realities concerning the relations between blacks and whites in Maycomb.

Even though the night before the trial Walter Cunningham had been among those who wanted take justice in their own hands and lynch Tom Robinson, Atticus "had a feeling" that after tangling with Atticus and Scout that night, the Cunninghams left with "considerable respect" for the Finches.  Atticus could have stricken the Cunningham kin from the jury, but, knowing that "once you earned their respect (the Cunninghams) were for you tooth and nail", he decided to take a risk.  Atticus had reasoned that "there's a faint difference between a man who's going to convict and a man who's a little disturbed in his mind".  As it turned out, the Cunningham relative was "the only uncertainty on the whole list", and he did indeed stand up for the truth by holding out in favor of acquittal for Tom Robinson (Chapter 23).

Atticus reveals that the jury took so long because there was at least one juror who took a long time to agree with the guilty verdict passed by the others; in fact, Atticus discloses that to begin with this man 'was raring for an outright acquittal' (chapter 23). Jem, who has been sorely disillusioned by the trial outcome, is astonished to learn that there was anyone on the jury that even thought twice about convicting Tom. However, he and Scout are even more amazed to hear who it was: one of the Cunninghams, who, prior to the start of the trial, had been part of a mob intent on lynching Tom. As Jem remarks with awe: 'I'll never understand these people as long as I live.'

The fact that the all-white jury took several hours instead of just minutes to convict a black man is taken as an encouraging sign by Atticus. Despite the ingrained racism of the town and the grim result of Tom's trial, there are hints that, however slowly, things might be changing. Certainly Judge Taylor himself comes across as quite sympathetic and, as Miss Maudie observes at one point, it was no accident that he picked Atticus, a genuinely fair and unprejudiced man, to defend Tom's seemingly hopeless case. And there are others in the town who appear similarly enlightened and free from the taint of racial prejudice, like Sheriff Heck Tate and the editor Mr Underwood. With such inhabitants as these, there is hope for Maycomb and for the future.

Following the guilty verdict brought against Tom Robinson, Jem believed that juries should be done away with.

"Tom's jury sho' made up its mind in a hurry," Jem murmered.

But Atticus disagreed and decided to set him straight. Atticus explained that it was "an inevitable verdict," one that usually takes an all-white male jury just a few minutes to decide. But Tom's jury took "a few hours." Atticus revealed that there was a single juror who held out in Tom's favor and, incredibly to Jem, it was a member of the Old Sarum crowd--a Cunningham, probably one of the same men who had come to the jail with the intention of lynching Tom. "On a hunch," Atticus had decided to not strike him from the jury, and though the man eventually succumbed to the pressure from the other jurors, he held out for several hours; had there been two Cunninghams, said Atticus, "we'd've had a hung jury."

Well, Atticus first has to convince Jem that they did take a long time.  Jem's initial opinion about it is, "Tom's jury sho' made up its mind in a hurry," and Atticus tries to convince him that actually, considering the case, they took quite a while.  There are times when it only takes a few minutes, but it took this jury a few hours.  He goes on to explain that "there was one fellow who took considerable wearing down-in the beginning he was rarin' for an outright acquittal", referring to a man on the jury who was actually fighting for the right thing.  Atticus didn't have much hope for a good verdict, but he was pleased that they took so long reaching the bad one.  He called that "the shadow of a beginning", which means the beginning of a change in people's set perceptions.  

In Chapter 23 of Harper Lee's novel To Kill a Mockingbird, Atticus is explaining to Jem and Scout how and why the jury that heard the rape case of Tom Robinson took longer than normal to vote to convict the defendant despite his being a black man accused of raping a white woman:

"That jury took a few hours. An inevitable verdict, maybe, but usually it takes ‘em just a few minutes. This time—” he broke off and looked at us. “You might like to know that there was one fellow who took considerable wearing down—in the beginning he was rarin’ for an outright acquittal.”

The juror who delayed the conviction for longer than usual in a case such as this was a member of the Cunningham clan, a "double first cousin" to Walter Cunningham, one of the leaders of the group that sought to break Tom Robinson out of jail in order to lynch him, but who was persuaded to back down by the innocence of Scout. As Atticus explains it to his children, he had earned the respect of the Cunninghams and, once that is accomplished, they will back you up in a challenge. This cousin of Walter Cunningham was sympathetic to Atticus' arguments in defense of Tom, but eventually had to acquiesce to the desires of the rest of the jury. 

In chapter twenty-three of Harper Lee's To Kill a Mockingbird, Atticus has a conversation with Jem and Scout (though Jem does most of the talking) about what took the jury so long to come back with a verdict in Tom Robinson's trial. The truth is that in any other trial in which a black man was accused of raping a white woman, the jury would barely have deliberated at all, as their minds would have been made up before the trial ever began. The fact that this one deliberated for several hours is actually a victory, despite the guilty verdict.

In Tom Robinson's trial, the jury was out for an extraordinarily long time. The day after the trial, Jem starts to talk with his father about juries in general and then about Robinson's jury. 

“Tom’s jury sho‘ made up its mind in a hurry,” Jem muttered. Atticus’s fingers went to his watchpocket. “No it didn’t,” he said, more to himself than to us. “That was the one thing that made me think, well, this may be the shadow of a beginning. That jury took a few hours. An inevitable verdict, maybe, but usually it takes ‘em just a few minutes. This time—” he broke off and looked at us.

Atticus then reveals another piece of information that surprises the children. One of the jurors "took considerable wearing down—in the beginning he was rarin’ for an outright acquittal." What is shocking is who the lone holdout on the jury was--a Cunningham.

Atticus took a chance and let one of the Old Sarum Cunninghams stay on the jury. He knows the Cunninghams have been stubbornly determined to do things they want and not be pushed around for many generations. Atticus also said:

the other thing about them was, once you earned their respect they were for you tooth and nail.

Atticus has the slightest hope that the Cunninghams had left the jail the night before (after walking away from a kind of stand-off with Scout and the other Finches) with at least a tiny bit of respect for the Finch family. Atticus hoped that would translate to some fairness on the jury. 

Then too, he said, it took a thunderbolt plus another Cunningham to make one of them change his mind. “If we’d had two of that crowd, we’d’ve had a hung jury.”

Jem is the one who really understands all of this; Scout simply reports their conversation. What we know from that conversation is that things might, just might, be starting to change in terms of racial prejudice. Those few hours of deliberation give us hope for the future.