The most important change that occurred in the New World as a result of the Columbian Exchange was the decimation of the population of the Americas.  The natives of the Americas died off in huge numbers as a result of the exchange.

The Columbian Exchange is not just about large animals like horses or plants like potatoes.  It is also about microbes -- germs.  The people of the Old World brought with them all sorts of epidemic diseases (notably smallpox) that the Americans had no resistance to.  As a result, "virgin field epidemics" spread across the New World and the majority of the native population died.

I would say that one of the major changes in the Americas as a result of Columbus was the introduction of slavery into the New World.  The Columbian Exchange began the process of legitimizing and sanctioning slavery as a way for nations to generate wealth.  The Columbian Exchange was one of the first instances of human trafficking and nations benefiting from it.  In the end, this helped to create a social order whereby those from European nations were seen as powerful while indigenous people were seen as inferior, needing to be subdued.  This helped to create a social imbalance in the Americas.  Along these lines, one of the significant changes that transpired in the Americas as a rersult of the Columbian Exchange was to associate colonization and advancement of European culture as being synonmous with control of other cultures.  This helped to create a racial and ethnic dynamic where both groups began to see the other in an adversarial light.