I think the following Romney quote defines in greater detail the idea of American Exceptionalism:
“This century must be an American century … In an American century, America has the strongest economy and the strongest military in the world. In an American century, America leads the free world and the free world leads the entire world.”
The idea itself posits (to boil it down to the basics) that America is exceptional – exceptional in the sense of “best, greatest, above everyone else”, etc. It’s rooted in nationalism and draped in the flag. Proponents of American Exceptionalism are often seen trying to impose The American Way on others (WW1 Wilsonianism through to forcing “Democracy” on Iraq) for their own good, because if it’s not American, it’s not right.