The main use is found in Super Smash Bros. for Wii U. There you can train his Amiibo by fighting against or with him.
> He can not control himself, but this was never alleged by Nintendo!
Amiibos learn from you and refine the fighting style and can also be personalized. However, much more intense than normal personalized characters. Can normal fighters only carry 3 items Amiibos by contrast fed (literally). You can all Power Up's cram into it, but pay attention to the values. A Amiibo with gigantic attack and a disastrous defense need not necessarily be a big hit)
Eventually your Amiibo is so strong that you can hardly beat him.
You can also take on a friend and let him fight against his Amiibo your Amiibo. Do you do this, so you get more experience and to learn more quickly than in the normal way. In addition, you will be rewarded with rare items that your Amiibo for you collect.
Moreover Amiibos can also be used in Mario Kart 8 or Hyrule Warriors. There, however, only for it unlock outfits or weapons. In future, it would still support the many titles Amiibos. Examples include Mario Party 10, Captain Toad Treasure Tracker, Yoshi Woolly World, etc.
Conclusion: see Amiibos class and fulfill its essential purpose really more than good. Thanks Nintendo!