Scout and Jem find several treasures including chewing gum, pennies, soap dolls carved to look like them, a spelling medal, and a gold watch. They were left there by Boo Radley.
The children begin playing a game the summer Dill arrives to try to make Boo Radley come out. They are fascinated by the local legend and act out his story. They are fascinated enough to try to make the recluse, who has never come out of his house, leave the comfort of his sanctuary. Clearly, someone is watching. Their message gets through, and one day the children fund gum in a tree on the corner of the Radley lot. They take it, and it becomes a kind of communication with Boo Radley. The shy recluse is saying hi, and although they do not know it at first, by taking the gum they are accepting his gesture of friendship.
Slowly, Boo Radley’s gifts get more valuable. He is childlike in his innocence, and does not have much to give. What he has, he gives. He adds to the list things like indian head pennies, dolls carved in Jem and Scout’s likeness out of soap, a ball of twine, an old medal he won in a spelling contest, and finally his gold watch.
Our biggest prize appeared four days later. It was a pocket watch that wouldn't run, on a chain with an aluminum knife. …Atticus said it would probably be worth ten dollars, knife, chain and all, if it were new. (Ch. 7)
These gestures of friendship are Boo Radley reaching out, and showing the children that he is there. At first they do not understand. Scout really doesn’t. However, Jem is old enough to realize what is going on. This is why is the most upset when Nathan Radley cements the knothole in the tree.
"Why'd you do it, sir?"
"Tree's dying. You plug 'em with cement when they're sick. You ought
to know that, Jem." (Ch. 7)
The tree is not sick, and Jem knows it. Nathan is trying to limit Boo’s contact with the outside world and the children, probably viewing it as inappropriate and not innocent. Jem doesn’t see it that way. He is offended, and sees the cementing of the tree as a cruel way of closing Boo in, keeping him in his prison for good.