From the Super Mario Wiki
North America is one of the seven continents of the world. It is featured in an episode of The Adventures of Super Mario Bros. 3, "7 Continents for 7 Koopas". When Bowser tried to conquer the entire Real World, he put Hip Koopa under control of North America. Hip used his magic wand to take over all of the TV networks, causing them to broadcast nothing but a Koopathon of himself, and refused to go off the air unless everyone in North America gave him all the money. Luigi later stopped him.
Because the United States of America is located within North America, all of the live-action segments of The Super Mario Bros. Super Show!, which are set in Brooklyn, naturally take place there, as well as a few animated episodes and part of the movie. Additionally, several other episodes of The Adventures of Super Mario Bros. 3 take place within the United States of America, and therefore take place within North America as well.