What is amiibo, you ask? It's Nintendo's foray into the "toy-to-life" category with collectible figures, or amiibos, that interact with the Wii U and its games. Nintendo showed off 10 amiibos at E3, including Mario, Donkey Kong, Pikachu, and others. You touch these characters to the Wii U gamepad to import character data into the compatible game you're playing. This is done through the magic of NFC using RFID standards -- there's a chip inside each amiibo that communicates in both directions.
The first compatible game will be Super Smash Bros. for Wii U. Following that, Nintendo's Mario Kart 8, Mario Party 10, Captain Toad Treasure Trackers, and Yoshi's Wooly World will all support amiibo interactions. Once they're activated in-game, the collectible figures will level up and gain special skills, adding a bit of role playing flair.
In regards to Super Smash Bros. for Wii U, every time your amiibo battles another character, it will get a small boost in abilities. Their attack and defense powers can go up and they can learn tactics to become stronger opponents. As you level up your amiibo and build a formidable character, you can use it to have automated battles with other amiibos (take it to your friend's house, for example, and battle his amiibo), manually battle friends/fores, or battle against your amiibo yourself.
There's a lot of customization taking place here, and it's certainly intriguing, especially if developers take advantage of amiibos in creative ways. But will it be enough to reinvigorate Nintendo? We'll find out later this year.