One critical element of the new Smash Bros game that is currently missing is Amiibo integration. Smash Bros will be the flagship title for Nintendo's new figurine initiative, but up until now, exactly how the figures will work in the game has been somewhat vague.
Now the official Smash Bros website has a breakdown, via Nintendoeverything. It seems that as you are starting a match, you can scan an Amiibo via the 3DS (or Wii U) NFC reader, and that character will load up on the character select screen. In this way they're like an assist trophy on steroids, or a specialized computer ally (or opponent, if you prefer).
The kicker is that these Amiibo "Figure Players" will level up, gain experience and even learn fighting techniques from human opponents. This info is subsequently stored on the embedded RFID chip in your Amiibo figure, essentially making that figure unique to you and the matches you've played.
Personally I'm a big fan of this approach because it makes the figures more meaningful long-term. Activision seems to be milking Skylanders for all it's worth, stamping out a new line of figures for every new game that you need to buy to get the most out of the latest Skylanders game. While the Skylanders figures do level over time their use is severely limited; there seems to be less and less emphasis on backwards compatibility with older figures, as Activision adds new gimmicks to each game like Swap Force and Trap Team figures.
I have no doubt that Nintendo will release specialized figures for new games--say, a Zelda or Samus figure specific to the latest game in those series--but the ability to store personalized data on these first Smash figures adds a lot of value.
Check Nintendoeverything for full details and screenshots of the new Amiibo system.