When I first looked around the Skyloft's Bazaar, I found a small sort-of backroom with a mysterious locked chest. Near the Scrap Shop, I think it was.
Fi told me that it was left there for me, specifically (neat!), but she had no idea how to open it.
How do I get that chest open? I want it.
Best Answer
Those chests are scattered all over the world above the clouds, and can only be opened by activating the corresponding Goddess Cube in the the world below the clouds with your Skyward Strike. Once you do that the chest changes colour and can be opened. When a chest has been activated by a cube, it will show up on your map as a rectangular shape .
This is a Goddess Cube:
Here is a map containing the location of two activated chests (indicated by the rectangular blue symbol):
Here is a picture of an activated chest, which is now able to be opened:
(images taken from: http://www.ign.com/wikis/the-legend-of-zelda-skyward-sword/Goddess_Cubes)