In story mode, there are quest as well as more open tasks, a city to construct and monsters to fight; basic fighting with normal enemies in real-time and boss-battles that require the right strategy. Collecting materials (e.g. dropped by monsters, from chopping wood, etc.) and finding specific items is at the center of the game.
I really enjoyed the game even though I never could get into Minecraft.
I hope there is an actual story for story mode. Not just extra quests or things to do.
Although from the trailer, it does look like there is a story or some sort with the hero building/climbing into the sky and looking off into the distance to the great evil (?) who (probably) has caused the need to build up the land again.
If that is the case, kind of sounds like Dark Cloud 2 (story-wise), and would be ok with that.