The first book, Harry Potter and the Philosopher's Stone, begins with the sentence: "Mr and Mrs Dursley, of number four, Privet Drive, were proud to say that they were perfectly normal, thank you very much." The ordinariness of the Dursleys is the perfect foil, the main counter-point to the magical world of Harry and Hogwarts. Making the wizarding world larger than life. The 'other' to our Muggle lives. The perfect adventure for children who are wont to believe in magic.
Harry carries the echos of the muggle world with him into the wizarding world. When he is unaware of things (like Quidditch, the gateway to platform 3/4, etc.) that a wizard would take for granted. When he gets startled by the moving pictures on the Chocolate Frog Cards. When he receives the 50 pence that the Dursleys send him for Christmas 'sellotaped' to the note.
When he is not intimidated by Voldemort's name, as it is just another name to him. Even if he is told that Voldemort is the one who killed his parents, he is not weighed down by the collective memory of terror that everyone in the wizarding world is.
"'...and until Hagrid told me, I didn't know anything about being a wizard or about my parents or Voldemort-'
'What?' said Harry.
'You said You-Know-Who's name!' said Ron, sounding both shocked and impressed. 'I'd have thought you, of all people-'
'I'm not trying to be brave or anything, saying the name,' said Harry. 'I just never knew you shouldn't'"
The protagonists of this book are at just the right age. Not only does the age match with that at which children in the UK start grade school, but it is ideal for the premise of the book. 11 is an age when children are able to be without their parents. It is also the age when they are able to handle the strangeness of new circumstances on their own. As it certainly would be for children which came from muggle backgrounds. It is also the age when children haven't yet come out of their childhood, and there is yet a belief in the possibility of magic. Again ideal for those from muggle households.
HP1 is very much in the mold of the school stories like Tom Brown's Schooldays, What Katy Did At School or the various school books by Enid Blyton. This appeals a great deal to children who find it familiar ground. With a difference, of course!