The Goddess Longsword is the second form of the Goddess Sword in Skyward Sword. Link obtains this sword after completing the Ancient Cistern and absorbing Farore's Flame into the Goddess Sword. With this upgrade, Link's sword is now longer and has double the power of before.
Throughout Link's quest, he upgrades the Goddess Sword to give it special powers and ultimately make it fit for battle against the Demon King.
The upgrades are, in order:
It is an upgrade over the Goddess Sword.