As everyone else said, I'm quite sure it's the Master Sword. I mean, it's hilt was purple, the cross guard had the same shape, it had that little widening of the blade near the cross guard, and it's sheath was very similar to the Master Sword's. What else could it be? Anyways, I'm pretty sure that Link had 6 hearts throughout the trailer, so maybe he'd already gone through the first three dungeons, and had just gotten the Master Sword. Whether or which, if there were six hearts, it's probably not the beginning of the game, so the Master Sword very well might not be what he starts with.
As for the whole Skyward Sword thing, you could take that a few different ways, but since they said something about holding the sword upwards to gain some sort of power, I imagine that's what it's talking about.