Approximately half way through the 20th century, history changes for the Harry Potter-verse. Gellert Grindelwald, who would have become one of the most infamous Dark Wizards of his time, was confronted by and subsequently battled the Dumbledore brothers Aberforth and Albus, just as happens in the canon universe. However, the results of this battle are what differ.

Ariana Dumbledore was not killed in the battle, Gellert Grindelwald was. Therefore Grindelwald never left England, he never stole the Elder Wand from Gregorovitch, he never built armies and terrorized Europe, he never built the wizard prison Nurmenguard to hold his enemies. In fact, Gellert Grindelwald never became anything at all, and very few historians even know of his name except in reference to the works of the very famous and very much still alive Headmaster Albus Dumbledore.

It is this little thing that changed all of history. A different Minister of Magic was appointed who had different rules and different office holders under him, and the Gaunt family, one of the families descendent from Salazar Slytherin, moved from their shack in Little Hangleton. Merope Gaunt never met the Muggle resident Tom Riddle, and so she never gave birth to Tom Marvolo Riddle, the man who would have later turned into Lord Voldemort.

Without Lord Voldemort, Harry James Potter was just a regular boy in a regular wizarding family without any particular specialness at all. His parents James and Lily Potter spoiled him rotten, and when he arrived to Hogwarts School of Witchcraft and Wizardry he was sorted into the House of Slytherin where he spent an unremarkable time at school, making average friends and average marks and doing average, normal, everyday boy things.