The most important characteristic that the United States contributed to the world during this time was its dedication to the idea of democracy.
When the American Revolution succeeded and the United States became an independent an democratic country, it was the most democratic country in the world. Its democratic system contributed to other revolutions that happened in the world during the time that you mention. Some examples of these are the French and Haitian Revolutions as well as the revolutions that led to the independence of Mexico and other Latin American countries.
Democracy did not start with the United States, but the US was the democracy whose example helped push more of the world towards democracy during the time period that you mention.