Vernon Dursley is a muggle, husband of Petunia Dursley, father of Dudley and uncle of Harry Potter by marriage. He used to live at Privet Drive along with his wife and son for nearly twenty years until they were forced into hiding during the escalation of the Second Wizarding War. After Petunia's sister Lily J.Potter and brother-in-law, James Potter, were killed by Lord Voldemort in their own home, Petunia remained the sole surviving blood relative of Harry's. Both Wizard and Muggle law demanded that Petunia and Vernon be the new legal guardians of Harry Potter, which they accepted (albeit reluctantly). However, they disliked Harry and treated him badly, while spoiling and fattening Dudley.
When Harry was sent a letter from Hogwarts School of Witchcraft and Wizardry, Vernon got very angry, as he detested anything to do with magic. He was a former student of Smeltings Academy and a director of the Grunnings drill manufacturing company. Vernon, Petunia and Dudley left their house in order to be hidden from Lord Voldemort and his Death Eaters (by the Order of the Phoenix.)