This is a great question, the kind of question that you could write a book about. We haven't got room for a book, so let's have a few quick possible answers.
First of all though , not every continent managed to develop like Europe. The Native Americans, the Incans, the Mayans, the Aztecs etc were all about 500 years behind the Europeans in 1500. In fact, oddly enough, I don't think the Aztecs ever managed to invent the wheel. The Aboriginies and the Maoris were on a similar level and China's decision to shut down their borders and scrap their navy stopped their technological advance at a stroke, mainly because....
1, Technological advancement is often the result of the kind of widespread exchange of ideas that only comes with immigration. Or emigration, depending on your perspective. In Europe, people moved about quite easily, particularly to England which has a good record of opening its doors to anyone in trouble like Jews, French aristocracy, fleeing Protestants and, in recent years, Blacks and Asians. New people, new ideas, new inventions. Africa is far bigger, the population is more spread out and long journeys are a far bigger pain in the arse.
2, War, as Trotsky once said, is the locomotive of change. Europe has been at war, in one way or another, on a near constant basis for 2000 years. Necessity is the mother of invention and, as Samuel L Jackson once said, when it's absolutely necessary to kill every mother ****er in the room, you need to be inventing some pretty tasty weapons. Europe got really good at the killing game.
Ultimately though, it's pretty tricky for a society to advance when some heavily tooled up white buggers turn up and take the strongest men away in cages to work on sugar farms on Santa Domingo. It gets even more difficult when they impose their own puppet governments, strip your nation of resources and take all the money back home with them. Then, to make matters worse, when there's no money to spend, they really **** you over by lending you some at nasty rates of interest, the kind of rates of interest that can only really be serviced by taking another loan....
Now, I'm not making this a blame-the-white-man game, but it has to be said that we haven't exactly helped.