Purpose of one-eyed statue in Skyloft?
It's relevant to the games story, so you don't need to worry about it for now. However, if you really want to know...
late game spoiler warning
After collecting the Song of the Hero, and completing the the Skyloft silent realm, you will receive an item that goes inside of the statues other eye. Doing this will reveal the final temple, containing the three pieces of the Triforce.