Dill and the Finch children have pretty much run out of ideas to stave off boredom for the summer holidays. But then, just when it looks like they'll have to sit around twiddling their thumbs all day, Dill suddenly gets a brainwave. He comes up with the Boo Radley game, in which the kids will creep up to the Radley residence and try to get the mysterious Boo to come outside.
Like just about everyone else in town, the children have never actually seen Boo. To them, he's a man of mystery, an urban legend, a kind of boogie-man figure with whom parents threaten their children if they step out of line. So if Dill's bold plan comes off then they'll finally catch a glimpse at this most unusual character.
Although the Finch children think it's an intriguing idea, Jem still has to think about it for three whole days before he'll actually take part. The reason is simple: he's scared. He's internalized all those horror stories about Boo to the extent that he genuinely believes that he might end up dead if he so much as knocks on the Radleys' front door. But Dill gradually wears down his opposition to the plan, playing on Jem's sense of honor by accusing him of being scared, which is perfectly true, as we've just seen, but of course Jem doesn't want to admit it.
Jem's acceptance of Dill's dare illustrates that he's growing up, which is one of the main themes of the story. Although the Boo Radley game itself in rather childish, the courage required to participate in it is not. Whatever the rights and wrongs of the game, Jem's participation in the game represents a rite of passage from boyhood to the adult world.