Hagrid says these words to Harry in Chapter 4, after bursting into the hut on the secluded island where Mr. Dursley has brought Harry to escape the magical letters. Hagrid’s surprise at Harry’s ignorance of himself and of his family underscores the separation of the Muggle and the wizard worlds. Being famous among wizards does not necessarily imply being famous among ordinary humans. Despite all the vast powers of the wizards, the Hogwarts officials have been unable to penetrate the defenses of stupid and selfish Muggles like the Dursleys, who have, quite impressively, kept Harry’s uniqueness a secret from him for ten whole years. The intense Muggle dread of being different and the powerfully oppressive denials of how Harry is special are actually quite a match for all the wizards at Hogwarts. In Hagrid’s astonishment that one could be a wizard without realizing it, we see how stifling and constraining human society can be, at least in the Dursley household.
Hagrid’s reference to Harry’s parents in connection with Harry’s own fame foreshadows one important aspect of Harry’s upcoming adventures. His experiences at Hogwarts will prove how talented Harry is (“You’re famous”), but they will also re-establish the connection that has been lost between Harry and his real family. By learning magic, Harry will earn the right to belong again in the company of his mother and father. Harry’s education will take him not just forward to his brilliant future, but also symbolically backward to his original family.