It's a common proverbial expression. To convey that some item, concept, or experience is a quintessential part of the American culture, you say that "x is as American as apple pie."
How did expression develop? How did apple pie come to represent the United States and its culture? Zachary Crockett explains in an article at Priceonomics. He traces the history of apple pie in English and American cookery. The earliest known recipe in the English language dates back to 1381. It was eaten in the American colonies by 1697.
But it took until 1902 before it came to define American culture. An English writer criticized Americans for eating so much apple pie. They should limit themselves to only two times a week. An unnamed New York Times editor responded:
“[Eating pie twice per week] is utterly insufficient, as anyone who knows the secret of our strength as a nation and the foundation of our industrial supremacy must admit. Pie is the American synonym of prosperity, and its varying contents the calendar of changing seasons. Pie is the food of the heroic. No pie-eating people can be permanently vanquished.”
Emphasis added because both pie and America are awesome.