Dragons are returning after they were thought to be extinct for many eons. They're ruled by an evil one called Alduin (meaning world-eater or smth). You play as the Dovahkiin (Dragonborn) and have the unique ability to absorb dragons' souls, killing them and gaining power to use for learning 'shouts' (different shouts have different effects, most are used in combat). Also, there's a civil war going on which you're allowed to pick a side in. You have to kill Alduin and restore peace to Skyrim.
All the fun is in the sidequests, though. There's lots of freedom, and you don't have to do the main quest if you don't want to.