From the Super Mario Wiki
Secret Island is a small secluded area appearing in New Super Mario Bros. U and New Super Luigi U. It is situated between Acorn Plains and Sparkling Waters, and can only be accessed via the world map's Cannon Pipes after the game is completed. The island only houses one purple Records Toad House, which itself contains various records, such as how many coins players have collected, how many Boost Blocks were placed, and so on and so forth.
Various flags, coins, Brick Blocks, Super Mushrooms, Yoshi Eggs, and Propeller Mushrooms can be seen in the background, along with the bags which contain P-Acorns. The ceiling is patterned with Nabbit-like silhouettes, implying that this place is Nabbit's hideout. Mario & Sonic at the Rio 2016 Olympic Games also directly references not only that this is Nabbit's hideout, but that he is the one updating the records.
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