In J.K. Rowling’s world, witches and wizards live alongside non-magical people in a ‘normal’ way, although they have a separate world unknown to Muggles. Unlike his aunt and uncle, Harry Potter was born with magical powers and his unusual abilities scare Mr Dursley and his family. That is the reason why magic is banned from being mentioned in the house.
Harry's mother, Lily, was born in a Muggle family and she discovered that she was a witch when, at age eleven, Hogwarts sent for her. At the school she met Harry's father, James Potter, and after they got married, she totally abandoned her Muggle life. Her sister, Mrs Dursley, never approved of Lily's choice so she always tried to keep her distance from the Potter family. When Harry's parents were killed by Voldemort, the Dursleys were obliged to care for the boy since he had no other family.