The European expansion into the North American continent brought a vast amount of wealth to Europe, concentrated mainly, but not exclusively, in the hands of Great Britain, France, and Spain. Because of differences in the governing structures of the three countries, Spain squandered most of its wealth, France place most of it in the hands of the monarchy and the aristocracy, and Britain, while hardly equalitarian, let some of the wealth slosh over and into the hands of a rising middle class.
France had so much power concentrated in the monarchy that it was able build and maintain a powerful military, which allowed it to maintain its status as a world power. Great Britain put vast resources from its colonial wealth into its navy, which enabled it to become the dominant naval power in the eighteenth and nineteenth centuries and the world's sole super power between 1815-1914.
In a nutshell, the enormous wealth that poured into Europe from North American allowed the Europeans to catapult away from the rest of the world in terms of technology, standard-of-living, and power—setting it up to dominate the rest of the world from the seventeenth century forward, with adverse effects on non-European cultures around the globe.
Crops and plants imported from the New World helped spur an agricultural revolution in Europe that led, along with other factors, to a population explosion. This led, in turn, to greater pressure to colonize North America.
In North America, the impact of the European arrival on native peoples was devastating, leading to widespread death through disease, warfare, displacement, and a wholesale destruction of cultures.