"Guns, Germs and Steel" is basically a summation of lower division world history survey courses. And it's the best explanation as of right now.
The Chinese weren't interested in exploration and conquering, largely for cultural reasons. There was one Chinese Empire which dominated the region, while there were many small European kingdoms, all trying to gain on advantage on their neighbors. This meant seeking out wealth and territory beyond their borders, which led the Portuguese around Africa to Asia, and led Columbus and the Spanish to accidentally run into the Americas. Of course, Columbus died thinking that he had found a shorter route to Asia, never knowing Hispanola was part of an entirely seperate continent. In the Columbian exhange of diseases, it so happened that small pox was more deadly and easily communicable than New World diseases like syphilis. Small pox had developed in Europe and Asia because of the domestication of sheep, goats and cattle and diseases like cow pox mutated to infect humans as small pox. Upon the arrival of humans into the Americas, all the large mammals that might have been domesticated all went extinct, with the exception of the llama in South America. But the Americas' north-south orientation meant that one form of technology (like animal husbandry with llamas) that was prevelant in the Andes, wasn't easily transferable to a different part of the continent which lay at a different latitude and had different seasonal patterns. Compare this with Europe and Asia, which has an East-West orientation, and vast amounts of territory all at the same latitude.
Furthermore, the fact that there were plentiful quanities and varieties of nutritious grains in the Fertile Crescent (modern day Iraq) meant that farming was easily feasible in this area and that technology quickly dispersed across the rest of Europe and Asia. And where there's settled farming and animal domestication, writing usually follows, allowing for better transmissiona nd documentation of ideas and thus more advanced technologies. Since there wasn't the same availability of grains or mammals for domestication in the Americas, farming and settled society was much more limited, and by the time of Columbus' arrival, Mesoamerica was the only part of the Americas in which writing has developed.
So the deadly diseases Old Worlders had developed from close contact with domesticated mammals, plus their guns developed from Chinese technology, mounted on horses and reinforced by steel armor, allowed Europeans to easily conquer and kill most of the Native American population. Few had time to adapt, but those that did, such as the Sioux, were formidable foes to American settlers.
This meant that Spain, Portugal, France and Britain gained vast quanties of arable land and large amounts of mineral wealth, and it's why their descendents still control the Americas today.
Europeans enganged in somewhat similar scramble for Africa in the 19th century, where conditions had favored limited farming and a more nomadic lifestyle for much of the continent, making Africans easy targets for European warfare technology, further increasing the wealth of European states. Only Ethiopia was able to successfully beat the European invaders and maintain their independence into the 20th Century.
So that's why.