Justice
The film is about a court case in which a young man is being tried for murder. If found guilty, he will get sent to the electric chair. As such, it is a very high-stakes case, and the jurors must ensure that justice is served. The jurors' duty as a group is to enact the law in the most just way possible, to tease out exactly what they have witnessed.
Throughout the film, we witness characters contending with their own definitions and standards of justice. These definitions vary a great deal, and the jurors' task is to talk things out and deliberate until a unanimous course of action can be taken in the service of delivering justice.
Doubt
When 8 initially votes "not guilty," he is the only juror to do so. The other jurors are flabbergasted, shocked that he would not perceive the case to be open-and-shut, as they do. He tells them that the reason he voted that way is not necessarily because he definitely believes the defendant is innocent, but because he sees "reasonable doubt." To him, the details of the case are too unsure for him to be convinced of the boy's guilt.
In the resulting discussion, the men talk about their respective convictions and doubts. Those who believe the boy is guilty are inevitably sure of his guilt, convinced by the evidence (however shaky) and confident about it. 8 acts and speaks from a sense of doubt, a knowledge that if he sends the boy to his death, he will be doing so without an adequate sense of confidence. So long as he has doubts, he cannot vote "guilty." Thus we see that it is doubt that motivates the entire narrative of the men's deliberation.
The Emotional vs. the Logical
8 is the epitome of cool-headed logic, arguing for the men to go through the logical steps of the case to determine whether there is enough evidence to support a guilty verdict. He wants to examine the facts and look at them from every angle to see what they can confidently determine about the case. His contrast is Juror 3, who reacts emotionally to everything and gets easily angered by the proceedings. His arguments are made in emotional appeals rather than appeals to logic. Thus, a major rift opens up between logical analysis and emotional conviction.
Violence
3 is defined not only by his emotionality, but by his violent tendencies. He tells the other jurors that children aren't respectful anymore, and then relates a personal story about seeing his own son run away from a fight and wanting to make a man of him. He tells them they got in a fight and his son hit him. They haven't spoken in 2 years.
Then, later, in the midst of their arguments about the case, 3 becomes increasingly annoyed and almost attacks 8 in a fit of frustration, but the other men hold him back. Here, we see that 3 has within him a tremor of violence—8 even calls him a "sadist"—that is causing him to have certain perceptions about the case.
Catharsis
3 is only delivered from his own irrational emotionality and violent tendencies at the end, when he experiences a cathartic response to seeing a picture of his son on the floor. He crumples into a vulnerable ball on the floor, ripping up the photo and weeping. Only after releasing his own emotions and being emotionally honest with himself is Juror 3 able to see 8's logic and agree that the defendant is "not guilty."
Prejudice
Prejudice is also a major theme in the film. In particular, Juror 10 has a strong bigoted attitude towards the defendant, who he views as worthless and inherently dangerous and guilty by virtue of being from the slums. At several points in the course of the meeting, he erupts into angry diatribes against poor people and immigrants. When he delivers a particularly nasty monologue, late in the meeting, many of his fellow jurors shun him, stepping away from the table in an act of resistance. "Prejudice always obscures the truth," 8 says.
Doing What's Right
8 does not stand up and insist on a discussion because he is a contrarian, or even necessarily because he is sure the boy did not commit the murder, but because he is committed to doing what is right. While the other jurors are satisfied to go along with the status quo and have a lazier approach to determining a verdict, 8 believes that they owe it to the defendant to go over all the facts and make a thoroughly determined decision. The other jurors complain about having to stay late and not continue on with their lives, but he slowly convinces them that doing the right thing is worth it.
