Columbus’s voyages to the Americas are important mainly because of the fact that they “opened” the New World to exploration and to conquest. In other words, Columbus’s four voyages did not have a tremendous impact in and of themselves, but they led the way to other voyages and events that did affect the Americas, Europe, and the world.
For the Americas, Columbus’s coming signaled doom for native societies. Native societies were almost universally destroyed or at least greatly altered by the Europeans who followed Columbus. The overthrow of the Aztec empire and the creation of New Spain is an example of this. The Aztecs lost their political independence. Culturally, they underwent a process in which their culture was mixed with that of Spain and became something entirely new.
For many native groups, Columbus’s coming led to eradication. This was particularly true in North America. There, English and other European settlers did not mix with native societies. Instead, they simply pushed them off their ancestral lands, killing many in the process. In addition, diseases brought by Europeans raged throughout the New World where people had no resistance, killing tremendous numbers of natives.
Columbus’s voyages also led to negative effects in Africa. Eventually, Europeans who came to the Americas decided that they needed labor to work their American plantations. They turned to Africa, and took millions of people from that continent to work as slaves in the New World.
In Europe, the effects of the voyages were generally more benign. Europe benefitted from many things found in the Americas. Spain, of course, got the use of American gold and silver. (This was not an unmixed blessing for Europe as it helped to fund many wars that might otherwise not have happened.) European countries gained an outlet for excess population, making domestic affairs less volatile as unhappy people could often simply leave for the Americas. Europeans were also exposed to such things as corn, potatoes, tomatoes, and chocolate, all of which changed their eating habits.
All in all, Columbus’s voyages led to events that affected almost the entire world. The effects did not come from Columbus’s voyages themselves, but from the later voyages and colonization that his voyages made possible.