One definition of "justice" is "the quality of being just; righteousness, equitableness, or moral rightness." As Twelve Angry Men begins, the jury made up with those twelve men is being charged with the task of determining justice in the murder trial they have just heard.
Justice involves treating everyone equally before the law. Some of the jurors bring with them preconceived ideas about youth and their actions that make it difficult for them to impartially evaluate the evidence presented during the trial. Others think differently about different individuals based on economic backgrounds, once again making it impossible for them to look at the individual being tried without bias.
As the jurors interact, it is not only the defendant who is looking for justice. The preconceptions of most of the jurors are also on trial as the twelve men debate what is "just" and "equitable" for all those involved in the case.