Okay, so the sun doesn't really have tornados in the same way that Earth does. But the shifting of warmer and cooler plasma across the sun's surface can create similar-looking phenomenon — in this case, a spiraling inferno as large as the Earth itself.
This "tornado" is caused by cooler plasma shifting back and forth above the sun's surface. Because the particles are being pulled by competing magnetic forces, we get the gyrating effect you see in the video.
What's especially remarkable about this video is that, just two years ago, we wouldn't have been able to observe the sun in such clear detail. It's only thanks to the Solar Dynamics Observatory, which launched in February 2010, that we see these solar events.