To try to answer this question, simply imagine what it would say about your town or city if you could walk “ten years, by night or day, for thousands of miles” without ever once meeting someone else who was also walking. What would that tell you about your town or your society?
In this case, it tells us that the setting of "The Pedestrian" is a society that has become bleak, desolate, and lonely. It has become a place where human beings no longer go out in public where they might meet one another in an informal setting. People have become so entranced by their technology that they no longer need one another and no longer want any human interaction.
In this story, as Mead walks, he is constantly thinking about what is on the televisions inside the houses. Clearly television is a major preoccupation of his society and the expectation is that people will stay at home and watch TV. Later, we even find out that there are no people in the police car. This is a society in which human contact is no longer desired. It is a society in which technology has taken over and destroyed the community of human beings that once existed.
By creating a setting in which a person could walk for thousands of miles through neighborhoods without meeting a single person, Bradbury is warning us about the negative consequences of having so much technology in our lives.