Nintendo figurines with NFC (near field communication) chips in their pedestals.
Put it on the WiiU GamePad, and it'll interact with Super Smash Bros., Mario Kart 8, Hyrule Warriors, etc. In Smash Bros., the figure comes to life as a computer-controlled character you can customize and train. They level up, boosting their strength and defense, and they have adaptive AI that learns from your fighting style. They also bring you loot at the end of each match, like custom parts and trophies. You can use them as sparring partners, team up with them, or pit them against your friends and their amiibos. Since they write to the NFC chip in the figure, the information is portable and can be taken with you to a friend's house, where they'll level up even faster.
And that's just Smash Bros. In MK8, they unlock special costumes for your Mii. In Hyrule Warriors, the Link and Toon Link amiibos will unlock a special weapon (the Spinner), while other characters will net you weapons, materials, rupees, etc. Amiibo support is also confirmed for Kirby and the Rainbow Curse, Yoshi's Wooly World, Mario Party 10, Captain Toad: Treasure Tracker, etc. All major Nintendo games going forward will probably support the amiibo figures in one way or another.
Currently, 12 characters are available: Mario, DK, Peach, Yoshi, Kirby, Fox, Pikachu, Link, Samus, Wii Fit Trainer, Villager and Wii Fit Trainer. There will be an amiibo for every character in Smash Bros. Other series will receive their own amiibo lines, although games will recognize a figure for its character (so the Smash Bros. Mario amiibo will still have some effect in Mario Party 10, etc., although the Mario Party Mario amiibo might have additional functionality).