In Chapter 8 of Harper Lee's To Kill a Mockingbird, Miss Maudie's house catches on fire, and Jem and Scout are ordered to stand in front of Radleys' gate, in safety, while the fire is put out. During that time, Arthur (Boo) Radley drapes a woolen blanket around Scout's shoulders since it's a very cold night, and no one notices. It's not until Atticus points out there is a blanket around Scout's shoulders that anyone figures out Arthur must have put it there. Atticus tells Jem to gift wrap the blanket so they could return it to him, but Jem protests because he fears for Arthur's exposure, knowing that his brother Nathan keeps Arthur on a very tight leash. Jem's protest leads to a series of confessions that induces Atticus to warn Jem not to inspire to "further glory."
The first thing Jem does when he realizes Arthur put the blanket around Scout is spill his guts to Atticus. He rambles on at rapid speed about all of the things Arthur left for the children in the knothole of the oak tree, about sneaking onto the Radley property to try and get a glimpse of Arthur through the window, and about finding his pants having been mended by Arthur. But, what weighs most on Jem's mind is the fact that, as he explains to Atticus, "Mr. Nathan put cement in the tree, Atticus, an' he did it to stop us findin' things" (Ch. 8). To Jem, Nathan's act of cementing the knothole is a certain clue that Nathan wants to prevent his brother Arthur from having all contact with the outside world, and if Nathan found out that Arthur gave Scout a blanket, Arthur may get into some sort of trouble. Atticus agrees that they should avoid exposing Arthur and says to Jem, "You're right. We'd better keep this and the blanket to ourselves. Someday, maybe, Scout can thank him for covering her up" (Ch. 8). But after having heard Jem confess to all of his antics concerning Arthur, Atticus next also says the line in question:
Do not let this inspire you to further glory, Jeremy. (Ch. 8)
In using the word "glory," Atticus is referring to all of the methods Jem has used to try and make contact with Arthur, such as trying to leave the thank-you note in the knothole and trying to get a look at him through his window. Atticus fears that since Arthur has again made contact with the children in his own quiet way, Jem might again begin trying to make contact with Arthur in Jem's own way, which really amounts to nothing but harassing Arthur. But, Jem insists he "ain't gonna do anything to him" and doesn't try to pull any further antics.