The police car repeats the word "walking" so much because it cannot comprehend that Leonard Mead would be out walking merely to enjoy the sights. It asks him what his purpose is in walking and treats taking a walk in the night air as deviant behavior. The idea of pleasure walking is so unusual it simply makes no sense to this robotic car.
The police car's trouble grasping the idea of taking a walk reinforces what the story has already established, that walking is a very odd activity in this culture. Everybody travels by car or spends their evenings sitting inside in front of their televisions sets. In years of taking walks, Mead has never seen another pedestrian.
The police car's incredulous reaction to the concept of walking helps us to understand that this society considers walking more than simply odd behavior. It is so strange that it is considered a symptom of insanity, and the police car whisks Mead off to the "Psychiatric Centre" for testing.
The story is a commentary on Bradbury's own society. In real life, he had been stopped and questioned by the police for being out taking a walk. This shocked him, because he grew up before World War II in a world where people frequently took walks or sat out on their porches at night and nobody thought anything of it.