The image of the folded pants symbolizes nurturing and loving care. Just as a parent might fold the pants of a child and leave it on the bed for him, ready to wear, so someone, whom the reader later discovers is Boo Radley, has neatly folded Jem's pants and left them for him to pick up later. The image is ironic, in that it suggests that things may not be exactly what the children expect them to be.
Jem, Scout, and Dill are terrified of Boo Radley, and the unknown (and perhaps imagined) dangers that lurk in his house. Although they themselves have never had the opportunity to interact closely with the him, neighborhood gossip and lore feed into the belief that unwholesome forces are at work in the house, and should be avoided at all costs. Their perception of the reclusive Boo is of a malevolent man who is a danger to them.
In reality, Boo Radley is a lonely man with a vast sense of humanity, and though he keeps himself hidden, he watches the children, and watches over them as well. He is the protector, as he proves later when he saves Scout and Jem from Bob Ewell's attack; the image of the folded pants symbolizes his benevolent nature, and foreshadows that, like a mother hen, he will take care of his children.
The repaired pants that are neatly folded and replaced on the fence where they were found represent the solicitude of Boo Radley for Jem.
Having been denied a carefree existence with the company of others, Arthur Radley delights in vicariously participating in the activities of the Finch children. For instance, in Chapter 4 Scout alludes to the day she rolled in the tire into the Radley front yard:
Through all the head-shaking, quelling of nausea and Jem-yelling, I had heard another sound so low I could not have heard it form the sidewalk. Someone inside the house was laughing.
So, having come to know something of the children, Arthur evidently finds pleasure in watching them and recovering some of his former delight in life through their experiences. Knowing that Jem will return for his pants in order to stay out of trouble at home, he repairs the torn pants. Like a big brother, Arthur looks out for Jem, and he also hopes that the children will continue to play where he can watch. After all, the children provide Arthur vicarious experiences that fill the voids in his life.