As you are reading a story, most often, characters have names. Because of this, the only way that a reader can relate to those characters is through other aspects of their personality, reactions to events, or their physical appearances. By using such generalized terms as "the man," and "the boy," that makes it easier for the reader to imagine themselves in that situation. Instead of the son being "Johnny," for example, he's just a boy; there are a lot more boys reading the book than Johnny's. So, it makes it easier for the reader to relate personally and imagine themselves or someone they know in those positions.
Another possible reason for not naming the characters is that it makes the story more universal; McCormac is saying that ANY boy, or ANY man in this situation could have this life. The themes are more universally applicable. The Road is less a specific story of a specific event, and more of a generalized commentary on humanity. A message in the book is that humanity has the potential for great evil and great beauty. To exemplify that point, he picks a simple father and son to elaborate. That makes the message more universal and general--more like a fable or a proverb, and less like a fictional entertainment story.
Lastly, terms like "the man" and "the boy" are consistent with the rather dreamlike, distant, aloof tone of the novel itself. McCormac has a very unique style in this novel, and that terminology supports and enhances that vague, distant style.
I hope that those thoughts help to get you started; good luck!