The correct answer is - politics.
The cities of the likes of Geneva, Brussels, and Washington, are all cities that have global political influence, thus they are considered as global cities, even though when compared with the other big influential cities they are only a drop in the glass.
The political influence is the main asset of this cities, so that is why they have their power. Geneva is a city where big portion of the global politics are decided and discussed by the big powers. Brussels is the city in which the EU politics are decided, thus it has influence on pretty much all oft he continent, but also in the world. Washington is the capital of the USA, still the most powerful country in the world in pretty much every aspect, so what is decided there, has global impact for sure.