The entire book Guns, Germs, and Steel is devoted to trying to answer this question. The basic answer, according to Jared Diamond, is that it was geographic luck that caused the general outlines of the distribution of wealth and power that we have today.
Diamond says that wealth and power came to those areas of the world that were first to develop farming. He says that farming was what made civilizations possible. Civilization, in turn, made it possible for people to develop technology such as (eventually) writing, steel weapons, guns, and sailing ships. Civilization was also responsible for the development of epidemic diseases such as smallpox. It was technology, along with epidemic diseases, that allowed Europeans to become wealthier and more powerful than people in other lands.
The people of Eurasia got farming long before anyone else because they had good geographic luck. They had many plants and animals that could be domesticated. The terrain of their land mass made it easy for farming and technology to spread. Because of their geographic luck, and because other continents lacked that luck, power and wealth came to reside in the hands of the Europeans, not in the hands of the natives of America, Africa, or Australia.