User blog comment:Curiousharry/what do wizards do, what is their purpose?/@comment-26051080-20150129100026/@comment-4836523-20150129124108

They live in the same world, but hide magic well enough that it's like an alternate reality. Exploring the books, films or even just the wiki might help explain that: simply put, wizards are Muggles who can use magic. In the books, wizards balance on broomsticks the way kids balance on those bucking bronco toys: sit on it normally while it flies around. These religions have spoken out against both Rowling and Hollywood for promotion of magic, but as Rowling has said repeatedly, the type of magic displayed in her books is entirely different from the "traditional" magic described as being anti-Christian. Indeed, several times throughout the books wizards are shown to be religious: James and Lily were buried in a churchyard, and it is suggested that they were attendees of the church, and Dumbledore (or someone similar, I think) owned a bible.