In the last paragraph of chapter 1, the author is trying to tell us that as the children are watching Boo Radley, he is watching them.
Chapter 1 describes the early history of Maycomb and the Finch family, and introduces the story of the neighborhood phantom Boo Radley. Boo (whose real name is Arthur) fascinates the children because he never comes out of the house. They have never seen him. They only know stories about him stabbing his father in the leg with scissors and creeping around the neighborhood eating cats and peeking into windows.
Dill likes the story, and decides to make Boo Radley come out. He dares Jim to touch the house, which Jim does. Then the chapter ends this way.
The old house was the same, droopy and sick, but as we stared down the street we thought we saw an inside shutter move. Flick. A tiny, almost invisible movement, and the house was still. (ch 1)
The house is characterized much like Boo Radley. It is sickly and dull. Yet there is a small flicker of movement, showing that someone is watching. The children are watching Boo, but Boo is interested in them too.
This incident serves to foreshadow the children’s involvement with Boo Radley throughout.
Boo Radley may seem like a secondary story line, but it is instrumental to one of the book’s major themes about the loss of innocence.
As the children get older, they realize Arthur Radley is a sad, lonely man, and not a monster. They slowly become friends, interacting with each other from a distance intentionally or intentionally. At perhaps the most difficult time in their lives, Boo Radley watches over them—and they watch over him.