The main amiibo functionality is with the Chibi-Robo amiibo. Scanning in it will activate Golden Chibi-Robo who is much more powerful than normal Chibi-Robo. After the player completes a level with Golden Chibi-Robo, it levels up so the player.
The other amiibo functionality is scanning other amiibos. These will unlock figurines of Chibi-Robo doing that pose.