From the Super Mario Wiki
Prince Mushroomkhamen was once the prince of Desert Land, but is now a mummy confined to a sarcophagus. His parents are Queen Mushroomkhamen and King Mushroomkhamen. As it so happens, Mario bears a great resemblance to Prince Mushroomkhamen. As the sarcophagus was never opened, the current, mummified state of Prince Mushroomkhamen was never actually seen.
The prince was stolen by Hip and Hop Koopa, which incited the rage of Queen Mushroomkhamen, who terrorized Desert Land in a rage. She later saw Mario, mistook him for her son, and forced him to take his place. In the end, the prince was found and returned to his mother by Princess Toadstool, Luigi, and Toad.