Because this is the first book in a series of seven, the author begins by setting the scene and introducing the reader to some of the characters who will be important through the books.
In the first few pages Rowling describes how in an ordinary suburb, somewhere in an English town, people who are leading their ordinary lives are suddenly surprised to see witches and wizards in odd clothing riding on public buses and appearing at places where people would not expect to suddenly meet a wizard. It is clear that something unusual has happpened in the world of witches and wizards, and those people, who are normally quite secret, are out and about, enjoying themselves.
In this way, Rowling introduces the two worlds of her story, the world of ordinary people, called "Muggles", and the secret world of the magic folk who usually keep to themselves. Rowling then introduces the main character, Harry Potter, a little baby boy who is left on the doorstep of his aunt and uncle by an old wizard with a long white beard.
When the reader next meets Harry, he has grown to be a boy of eleven, living unhappily with his spiteful aunt, cruel uncle and bullying cousin Dudley. Suddenly he is rescued from his misery by a huge half-giant man with a great black bushy beard and a flying motorcycle. Harry Potter is a wizard without knowing it, and the giant man, Rubeus Hagrid, has come to help him buy his books and get ready to go to school. The school sounds most exciting. It is "Hogwart's Academy of Witchcraft and Wizardry".
On the long train journey north, Harry Potter meets the two people who are to become his best friends, Ronald Weasley and Hermione Granger. Ron and Hermione have very different characters. Hermione, who comes from "Muggle" parents, is very intelligent and talented. She is such a know-it-all and so bossy that the boys do not like her at first. Ron, on the other hand, comes from an old family of wizards. He is number six in a family of seven children. He wears hand-me-down clothes and even his pet rat used to belong to his brother Percy. Ron knows all about Harry Potter.
The reason that Ron, and all the other people in the wizarding world, know all about Harry Potter is that Harry is famous, without even knowing it himself. The reason why he was left on the doorstep of his aunt and uncle is that both his parents are dead. They were murdered by an evil wizard who calls himself "Lord Voldemort". He is so evil that people are even afraid to say his name. Harry is famous because he survived the magical attack of the "He who must not be named", and since that day, Voldemort has gone into hiding.
Joanne Rowling then gives the reader a picture of the school that is to be Harry's home through seven books of the series, each one of which deals with a year in his life. The book describes the teachers, the lessons, the customs and the school sport so that it seems to be part of a real world. Even though the students learn magic and use magic, the book also describes Harry's growing up in a new and strange situation, just as any student must learn to fit in when they go to a new school among different people.
Harry soons discovers that while some magicians, such as the School Principal, Professor Albus Dumbledore and Deputy, Professor Minerva McGonagal, can be kind and encouraging, others, like the sinister Professor Snape with his greasy black hair and nasty comments, are very hard to trust. One of the subjects that Harry really needs to learn is "Defence against the Dark Arts" but unfortunately, the teacher, Professor Quirrell, is such a bumbling and nervous man that he does not seem to be able to teach Harry very much at all.
As the year goes by, Harry discovers that Hogwart's has, hidden away for safety, a very precious treasure. If it were to fall into the hands of Lord Voldemort, it would be very dangerous indeed. Harry also discovers that in solving problems and overcoming difficulties, having friends with very different talents can be extremely useful.