From the Super Mario Wiki
North America is one of the seven continents of Earth. It is featured in an episode of The Adventures of Super Mario Bros. 3, "7 Continents for 7 Koopas". When Bowser tries to conquer the entire Real World, he puts Hip Koopa under control of North America. Hip uses his magic wand to take over all of the TV networks, causing them to broadcast nothing but a Koopathon of himself, and refuses to go off the air unless everyone in North America gives him all the money. Luigi later stops 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 Super Mario Bros. film. 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.