From the Super Mario Wiki
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The amiibo Hut is a building appearing in Yoshi's Woolly World, located on Craft Island. Here, Yoshi can change into a variety of skins that can be unlocked by scanning certain amiibo. For example, a Mario amiibo unlocks a design that resembles Mario. If the player scans a Yoshi amiibo, Yoshi can turn into a non-woolly version of himself. The Super Smash Bros. (except the Pokémon and DLC characters), Super Mario and Splatoon series amiibo are all compatible with Yoshi's Woolly World. Another similar hut, the Yoshi Hut, contains designs that are unlocked by collecting Wonder Wool in the game.
A list of Yoshi's amiibo designs can be found here.
"Once you load an amiibo, its design will live here, so come anytime to swap your design!"