from what i can tell, you can have a conventional magic spell equipped, and then you can have a dragon shout equipped too... dragon shouts are pretty much the same thing as magic, but you have to learn them by finding dragon writing around the world, and you unlock them with dragon soul points.
you're something called a dragonborn meaning you have some special connection to dragons. Dragons used to be dormant but now they're coming back to life and you have to deal with that. Add to this a million side quests and political assassinations and you have skyrim