The setting of a story can help define and shape the character for the reader. For example, the character living in a trailer at the beach working odd jobs obviously has a different set of goals than the character working as a business executive living in a downtown condo. Despite all the other descriptors that the story might have regarding the characters, the place and time of his job and home help to define him for the reader.
The characters in Charles are shaped by the family home in the first part of the story. We read that Laurie (who we later find out is Charles too) walked off toward kindergarten with an older friend, rounding a corner without saying goodbye. He walked in the front door at lunch, throwing the door open and tossing his things down. We visualize a middle class child and family in these characters. As for Laurie, his actions reflect a confident in his relationships with his family, living a comfortable life based on these settings. The fact that he walks home from school for lunch hints that Laurie and his family may live in a past time when this was the norm. Descriptions of the school such as the mention of a blackboard and standing in the corner, further reflect that the characters live in the past.
Some of the descriptions of the setting reflect the mother's character too. There are many mentions of her walking Laurie down the sidewalk, sitting outside the home waiting for him and mention of her going to the PTA meeting. These all reflect that the mother from whose point of view the story is told, is a very involved and responsible parent.