This is a good question. Because Jem is old enough to understand what is going on, he is intensely interested in the trial.
Atticus offers a brilliant reconstruction of what most likely happened during the trial. When Atticus shows that Bob Ewell was left-handed, Jem thought that the jury would surely see that he was the one who hit his own daughter, Mayella. Jem, at this point, says, "We got him."
When the verdicts came in "Guilty, Guilty, Guilty," Jem was mortified. Here is what Scout observed:
I peeked at Jem: his hands were white from gripping the balcony rail, and his shoulders jerked as if each “guilty” was a separate stab between them.
Jem was in disbelief, and he realized that the world, even Maycomb, his beloved town, was far from a perfect place. More particularly, he realized that Maycomb was a racist place where race trumped justice. This is why he repeatedly said that what had happened was not right. For Jem this was a coming of age experience, when he realized that the world could be a harsh and unjust place. This was one of the saddest parts of the book.