Although we can look at many changes that both directly and indirectly took place as a result of Columbus's voyages to the New World, it helps to define them through three main categories: the environmental, cultural, and political impacts.
Once Columbus found a passage west and opened up trade with the Americas, an exchange of crops, plants, animals, and diseases took place, which called the Columbian Exchange by historian Alfred Crosby. Through this exchange, many important foods came to the "Old World" of Africa, Europe, and Asia, most notably corn, potatoes, tomatoes, and manioc (cassava).
However, for the "New World" of the Americas, Afro-Eurasian plant species dominated the indigenous species, leading to some serious ecological changes. Worse than that, the Indigenous people of the Americas, geographically isolated from Afro-Eurasian peoples for tens of thousands of years, did not have immunity to many diseases. Historians estimate that anywhere from ninety percent of all Indigenous peoples in the Americas died from diseases as a result.
With a weakened population, the Europeans were able to conquer much of the land. Culturally, we see a huge push in Christianity. Beginning first with Spanish and Portuguese Catholic priests, there was a widespread effort to convert the Indigenous populations of the New World, and its effect is evident when looking at the religious makeup of the Americas today.
Politically, many of the powerful, existing empires in the Americas were conquered by the Spanish. The two most famous examples are the Aztecs of central Mexico and the Inca of the Andes Mountains, centered on modern-day Peru. These empires, though advanced and powerful, did not have access to the same technologies that existed in Afro-Eurasia, most notably iron, guns, and gunpowder. When the Europeans arrived, a combination of these deadly weapons and the deadly diseases ensured European victory over these powerful American empires.
As a result, the Americas were largely colonized by the seventeenth century. Northern European empires, like the British, French, and Dutch, soon followed the Spanish and Portuguese. Though many of these actions took places a long time after Columbus's initial voyages, we can trace direct lines from Columbus's journey to the changes that impacted the Americas.