At first I was like "oh god this is awkward" but I understood perfectly. She was saying that in Roman / Greek history performing for the greatest athletes was quite the honour, and being that she's Italian American (coming from Rome, the epicentre of the Roman Empire) it was super exciting to have this same honour, but in America. The "I'm European...as an American" was a little confusing at first though.
I watched this yesterday and I screamed She was drunk, she literally snapped a picture of her drinking wine 1 minute after she got off the stage singing the NA