FrostyChick said:
I'm pretty sure it's caused by inheriting a small fragment of the divine spark of Akatosh. It's normally very, very rare. And it's only handed out to maybe one or two individuals at any given time. This is of course based on prophecy and the whims of the god himself.
In the series timeline the most recent (documented) Dragonborne would have been Martin Septim.
It is inherited through blood, so if it's given to one person, then the rest of their lineage will have it. Hence why there was the big concern in cyrodiil when the Spetim bloodline ended at the end of Oblivion.
Generally it's a sign of that the individual will play an important role in history.
This. It's more than possible for the Septim bloodline to have skipped a few generations or for some Septim descendants to have bred or wed outside of Imperial bloodlines, so this could explain why Skyrim's Dragonborn could prospectively of any race or background. What helps is that the Empire has been losing its sense of direction since the end of the Third Era. Based on what's available online, you get the sense that the Imperial Legion is a corrupted shadow of its former self. I wouldn't be surprised if Ocato was still in power and basically gave the finger to the entire Elder Council, soon after the end of the Oblivion Crisis.
Considering this, your character could feasibly have some distant relationship with the Septim bloodline and have inherited a speck or two of Akatosh's power, regardless of his race or gender.