There is too much to state, but I will say some of the easiest would be:
The Physics Engine. Now there is so much more possible to do and in many combinations, that I suspect that I probably will be doing tons (and hours) of exploration, going into nooks and crannies and seeing what wicked stuff I can do with the Shieka Slate.
The Mystery. Zelda has had mystery before, but now I'll get to discover what has happened on my own and at my own pace, instead of having it spoon-fed to me.
Just Having the Little Things. Being able to take damage in the cold if you're not wearing clothes, finding food and cooking it in different combinations to restore health and stamina, finding various minerals, and using various weapons (and being able to keep them until they break) makes the environment feel much more rich and inviting.
The Enemies Have Some of the Same Abilities You Do. The Bokoblins can tame and ride horses like you, they can use fire against you, and they can pick up various weapons like you, even go hunting if they think you aren't there. To me, that makes them immensely interesting (and even suggests they have their own 'culture,') as opposed to past enemies that simply wait around and do little until you kill them.