In chapter 1, Jem has a fantastical perception of Boo Radley that isn't even human:
Boo was about six-and-a-half feet tall, judging from his tracks; he dined on raw squirrels and any cats he could catch, that's why his hands were bloodstained... There was a long jagged scar that ran across his face; what teeth he had were yellow and rotten; his eyes popped, and he drooled most of the time.
This description is a cross between some feral animal and a character resembling Frankenstein's monster. The kids develop a morbid fascination with the legend of Boo, and it is easy to invent games with him as a central character because they don't view him as a real human being—he is more myth than reality. Thus, they sneak around his house at night and play in the yard, pretending to be Boo stabbing his father with a pair of scissors.
Yet this idea of Boo changes with time. Gifts begin appearing for the kids in the old tree, and at first they cannot determine where the trinkets could be coming from. One day, it strikes Jem that Boo could be leaving he gifts, as he pauses to look at the Radley house with great consideration.
After Jem and Scout find soap carvings that appear to be replicas of themselves in the hole and then discover a pocket watch with a knife, Jem realizes that Boo Radley is leaving the gifts. He cannot figure out why Boo would do such a thing, but he wants to thank him.
These offers of kindness, presented without any need of acknowledgement or recognition, transform Jem's perception of Boo Radley. He no longer sees Boo as a semi-human of morbid fascination but as a real person with real needs for human connections, just like anyone else.