That is Greba, a wise old woman.
Greba is an old woman who lives on Skyloft with her son Gondo in Skyward Sword. Greba and Gondo live in the same house, and while Gondo goes out during the day to run the Scrap Shop, Greba is always seen at home. Greba spends quite a bit of time washing Gondo's dirty laundry during the day, and frequently complains about her son's constant filthy messes and tinkering with machines, as she always has to clean it up.
Greba concept art from Hyrule Historia.