From the Super Mario Wiki
Asia appeared 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 Bully Koopa under control of Asia. Bully vandalized the Great Wall of China by spraying graffiti all over it. Mario later stole Bully's wand, and turned the Wall into a giant dragon, who terrorized Bully.
Also, the events of Mario & Sonic at the Olympic Games take place in this continent, because it is where Beijing is located. Beijing is People's Republic of China's capital city and hosted the 2008 Summer Olympics.
In their common language, Asia is translated in these ways:
 Names in Other Languages