Harry Potter and the Sorcerer's Stone is narrated in third-person limited point of view. Third-person narration is simply when the narrator uses "he/she/it/they" when telling the story. This is what occurs in the entire Harry Potter series.
While it may get confusing when you read quotes in the book of Harry saying "I," that is simply the narrator quoting Harry. The first time the reader meets Harry in the Sorcerer's Stone is an example of the third-person limited when Rowling writes on page 19, "He rolled onto his back and tried to remember the dream he had been having." The word "He" lets you know immediately it is third-person.
To be more specific, the point of view can be called "third-person limited". Essentially, this means the narrator can describe to the reader the feelings and thoughts of the main character but not the surrounding characters; this power is limited to the main character only. This is exactly what J.K. Rowling does for Harry in the series when you read passages that describe Harry's thoughts and Ron and Hermoine's actions. For instance, on page 130, Rowling writes, "Perhaps Harry had eaten a bit too much, because he had a very strange dream." These were Harry's thoughts while in the presence of other characters.