Amiibo is Nintendo's wireless communications and storage protocol, for use between compatible Toys-to-Life items and the Nintendo 3DS and Wii U gaming platforms. These toys use near field communication (NFC) to interact with supported video game software, potentially allowing data to be transferred in and out of games and across multiple platforms.
Amiibo toys can be used directly with the Wii U GamePad and New Nintendo 3DS series, while an adapter for the rest of the Nintendo 3DS series was released.
Source: Wikipedia, "Amiibo", available under the CC-BY-SA License.
Amiibos also work with Nintendo Switch. After activating the Amiibo Rune, touch the bottom of the Amiibo to the top of the right joystick.