After convincing the jury to give a Not Guilty verdict, Juror #8 walks over to #3, his nemesis, and puts his coat on for him. The gesture shows us that despite the extent to which they've argued in the jury room, there will be no hard feelings once they head back into the world.
Juror #8 then runs into #9 outside the courthouse, and they tell one another their names, which totally reminds us that we haven't heard a single person's name in the whole movie—and that counts for all twelve jurors, the "kid" on trial, "the old man" witness and the "woman" witness. This lack of names helps us realize that democracy isn't about the individual; it's about the group and its ability to make good decisions.
It's a little more complicated than that, of course, because it is one individual who saves the day and directs the group of jurors to justice. But he's the one who best understands his duty as a jury member, which is the make sure the group actually serves justice.
In the final shot of the movie, we see Juror #8 walking away from the courthouse with a big smile on his face. The shot reminds us that even though things looked bleak for a long time, the system can work if people take it seriously and put their prejudices and self-interests aside.