New compared to previous games or new as in the Welcome Amiibo update? Regardless, the most interesting new thing in New Leaf I would say is the island, with all the minigames and whatnot. Everything else is about the same but better.
If you are talking about the Welcome Amiibo update, here is the direct from it. The UK version has a little more info regarding the island and compatible amiibo cards released over there and Japan. With the online island you can leave more easily if someone tries initiate a tour, to prevent your exit. There is also a handy mute feature for there as well.
Well you have 2 more shop upgrades, T.I.Y and T&T Emporium which requires you to pass Gracie's fashion checks to unlock
You can fill your museum to 100% which means finding all the fossils, bugs, fish, and genuine art from Redd
You can collect the nintendo fortune cookie items if you're into that
You still need the fortune shop which means you have to get i think 20 fortunes told by katrina in her tent
... and the rest is really just up to you! You can theme your houses and try and buy items to fit them. You can spend ages landscaping and unlocking PWP's using the diving trick, you can collect all of Phineas's badges and also Shrunk's "jokes"(he gives you emotions/poses you can use in game)
Plus I'm sure there's more but this is just off the top of my head