I'm not familiar with the manga or the games at all, but I'll try :
- the story begins when Luffy and friends are attacked by a mysterious structure emerging from the sea
- new designs are supervised directly by the original mangaka
- each stage start at the landing point. You're free to go back to your ship (which serves as a base) at any time.
- main starting goals : collect items while fighting minor enemies
- you can trigger missions if you feed some items to the weird little creature called Gaburi that Luffy has with him.
- some bosses will fall from trees as some sort of nuts, which will then turn into a gigantic creature. Once you defeat it, it turns back into a seed, which you can turn into a treasure by feeding it to Gaburi
- feeding Gaburi to make him grow is very important to the plot
- once you clear the stage you're then able to proceed to the next stage, but you can replay the stage you've just cleared as well
- Two new shortcuts systems : a cannon that shoots you from your ship to any island you've visited, as well as a giant slingshoot that allows you to go from the island to your ship.
That's pretty much it.