Jem is forced to make an unexpected solo mission to the Radley Place one night to retrieve his lost pants. Earlier in the evening, Jem, Scout and Dill had made it as far as the Radley porch, from where Jem tried to peer in a window. But, suddenly, a shadow appeared, and the children prepared for the worst. But just as quickly, the shadow disappeared, and the kids sprinted for safety as a shotgun blast rang out. However, while crossing a wire fence, Jem's pants became entangled before he finally pulled free. When the kids joined a group of people who had gathered in the street to discuss the noise (a Negro was suspected of the mischief), Miss Stephanie realized Jem had no pants. He had lost them in the fence.
Knowing that Atticus would want to see them in the morning, Jem knew he had to retrieve them that night, in part because "Atticus ain't ever whipped me since I can remember. I wanta keep it that way." He made it safely back, but the next morning he had an even more unusual story to tell Scout.
This is a good question. It is clear that you have an eye for detail. The significance is twofold.
First, this act of going to the Radley house at night by himself shows his courage. Jem is growing up. This is one of the main themes of the book. There is development in nearly all the central characters.
Second, as the previous post says, Jem needs to get his pants back, but the significant point is that he got them back and they were fixed. This odd details shows that the person who fixed these pants might be Boo. In the reader's mind, Boo might not be a frightening man at all. Jem and Scout also may need to rethink what they think about Boo.
From these two perspectives, Jem's lone trek to the Radley house is a transition for the children and Boo Radley (and also the reader).
In Chapter 6, the creative Dill challenges Jem to go onto the Radley porch with him and try to see inside. Their plan goes awry when Mr. Radley fires his shotgun on the porch; terrified, the boys take flight, but Jem catches his pants on the Radley's wire fence. In his haste to get to safety, he wriggles out of them and runs only to be stopped by the neighbors who have assembled outside, having heard the shotgun blast. When Atticus sees Jem standing in nothing but his shorts he asks him where his pants are. Jem stalls, not wishing to lie; however, Dill tries to cover for him, telling Atticus that he has won Jem's pants playing strip poker by the fishpool. When Dill's Aunt Rachel is shocked that the children were playing with cards, Jem continues the lie and says that they were using matches.
1. Once they are home, Jem feels that he must retrieve his pants before his father learns that he has lied. While he shakes from fright at the thought of returning to the Radley fence for them, Jem is even more worried about the repercussions of having lied to his father. He tells Scout,
"Atticus ain't never whipped me since I can remember. I wanta keep it that way."
Jem ventures out and returns after a while; however, Scout can tell that he is trembling as she hears his cot moving.
2. Later, Jem tells his sister that when he returned for his pants, he found them neatly folded over the fence as though he were expected to return for them, and they had been sewn, as Jem says,
"Not like a lady sewed 'em, like somethin' I'd try to do. All crooked. It's almost like--"
"--somebody knew you were comin' back for 'em."
Jem shuddered, "Like somebody was readin' my mind."
This is the first of Boo Radley's kind gestures.
When Jem has to go back in order to get his pants he has to go by himself and warns Scout not to tell her father. On top of that, when he goes back he realizes that someone must have sewed them together and knew he would be coming back. While reading the story it causes us to consider whether or not Boo Radley did this.
He had to get his pants so he wouldn't get whipped by Atticus.