>>19683105They work similar to the rumble figures in that you can train up a character and save it on there, so you can take your saved characters over to a friend's house (in before "but I have no friends...) and use it to battle them, or team up, on his or her games.
However, in addition to what the rumble figures can do these figures will work across many different future nintendo, and possibly 3rd party under licence, games too and have different effects. For example as well as Smash Bros they'll work in Mario Kart 8 but it hasn't been specified what they'll do, it could be that the Pikachu one will activate a lightning bolt for example or they could give boosts to kart/driver stats or even access to new drivers.
In Smash it has been said that they may even save your fighting style with a character so you can battle yourself or team up with a friend to battle yourselves on your friends WiiU.
Also with the adaptor coming out next year for the 3DS it would not be surprising if some sort of compatibility was not already programmed into ORAS on their release, maybe even a series of pokemon amiibos will come out at the same time as the 3DS adapter to promote it.