This happens in Chapter 25. What Jem says to Scout is that the caterpillar (a roly-poly, is the word they use) never hurt her so why should she hurt it.
Scout feels like Jem is getting weird. She asks him sarcastically if he's going to stop killing mosquitos and flies as well.
The significance of this episode is that Jem is feeling bad about what has happened to Tom Robinson. He thinks that the bug, like Tom, is just some innocent thing and that means it is not appropriate to kill it.
Like Tom Robinson--and the mockingbird--the caterpillar which Scout was about to smash was a weak and defenseless character. Jem was still reeling from the guilty verdict which sent Tom to prison, but the news of Tom's death was almost more than Jem could take. "They don't bother you," Jem said of the roly-poly that Scout was preparing to kill. Scout's reaction was that Jem was the one who seemed to be acting more like a girl. She wondered if Jem was "crazy," and if he soon would be defending mosquitos and redbugs as well.
Jem believes that just like Tom Robinson, bugs are important and should not be killed since they are innocent. He is affected by the case and as Jem matures he starts to incorporate his father's ideals and the importance of thinking everyone is equal. The theme of the mockingbird appears as Tom Robinson is shot down even though he is innocent, and Jem sees the innocence in the bug and does not want to kill it. Then Scout thinks Jem is crazy and starts wondering if he'll defend mosquitoes next
Once again, this reocurring theme of the innocent mockingbird appears. The mockingbird has done nothing but sing lovely melodies for people to hear, therefore it should be considered a sin to kill a mockingbird (hence the title of the novel). This caterpillar (or roly-poly) serves a similar role to that of the mockingbird in that it has done nothing to Scout yet she decides on a whim to end its life. This roly-poly, like the mockingbird, symbolizes the powerless black community who are constantly scapegoated and bound by the color of their skin. The black community has done nothing yet is constantly stereotyped and viewed as inferior to whites.
Jem is becoming more like that of Atticus as he grows and matures: he begins to understand that the testimony of an African-American will always be ignored and that the whites, no matter how morally corrupt, will be considered more pure than any African-American. He intercedes on the behalf of the roly-poly and asks Scout to spare its life as it has done nothing to her.
This passage portrays many aspects of the novel in that the roly-poly, through one perspective, could represent the innocent and powerless Tom Robinson. The hand of Scout that strikes down is similar to Mayella Ewell's harsh, stoic accusation of rape against him.