There shouldn't be a story mode. As far as I know there will be a retail disc copy to purchase. I kinda know from working at a little known game store. You basically create platform levels and share your creations online with strangers or friends to play through. It looks pretty fun and apparently will be updated with new features often.
A story mode could be possible, it wouldn't be too outrageous. Where you progress through the levels to save someone or something and have to kill bosses and solve puzzels etc. But, I think the main part would be in the creation and sharing of user created content.