A horizon, by definition, is permanently beyond reach. As Henry Kissinger was a pretty exceptional diplomat as well as an intelligent individual, I don't think he believed that we could ever achieve a utopia.
I interpret his quote to mean that America is an idea and an ideal. I think he meant that our pursuit of that ideal, and the hope that is the idea of America is what makes us different from other nations, and in his mind, great. As a Jewish refugee from Hitler's Nazi Germany, Kissinger perhaps had a more idealized perspective of our country. The fact that he rose through the ranks in his adopted land to become a trusted adviser to the President of the United States probably made the ideal and the hope seem closer and more realistic to him than perhaps it would to others.
America is typically seen as a country of optimists. As the article linked below (from Forbes Magazine) shows, Americans typically feel better about themselves and their futures than people from other cultures do. This is what Kissinger is saying in this statement -- he is saying that we Americans always believe that our country is improving and that we will achieve perfection soon.
This sort of attitude can be seen at various times in our past. We continually have movements where people try to perfect the society they live in. We have the reform movements of the 1830s and 1840s. We have the Progressive Movement of the early 1900s. We have efforts like Lyndon Johnson's "Great Society" where we believe that we will be able to eradicate various ills.
For our history, we Americans have been optimistic. Henry Kissinger captures that aspect of the American spirit in the quote that you provide.