Why does Jem follow Atticus out of the house that night?
In Chapter 15, the townsmen come and stand in the front yard of the Finch home. Atticus must go outside and talk to them as they wish to confer with him because they anticipate problems regarding the upcoming trial of Tom Robinson. When Atticus questions what he feels is unwarranted concern, Link Deas speaks up,
“Nobody around here’s up to anything, it’s that Old Sarum bunch I’m worried about… can’t you get a—what is it, Heck?”
“Change of venue,” said Mr. Tate. “Not much point in that, now is it?”
“Link, that boy might go to the chair, but he’s not going till the truth’s told.” Atticus’s voice was even. “And you know what the truth is.”
After the men leave, Jem expresses his fear for Atticus. On the next day, Sunday, the men talk to Atticus outside the church, informing him that Tom has been moved to the Maycomb jail. That evening Atticus tells his family that he is going for some "exercise," but he takes the car. This odd circumstance worries Jem since he is aware of the earlier concerns and conflicts of the townsmen. Instead of going to bed, Jem dresses and tells Scout, “I’ve just got this feeling,” Jem said, “just this feeling.”
"This feeling" proves to be correct as the Old Sarum Bunch pulls up to the jail where Atticus sits in a chair propped against the jailhouse door. The single man, Atticus, faces this angry mob, and his daughter diffuses the tension while Jem stands beside him, offering his filial support. Finally, Scout talks to Mr. Cunningham who becomes ashamed and breaks up the group after Scout asks him to mention her to Walter, his son. In gratitude for his son's loyalty, Atticus rubs his head.