The Hero's Spirit is Link.

[retrolinkx]

The Hero's Spirit is an undead (assumed Staflos) specter who helps the Link in Twilight Princess by teaching him hidden sword skills and even songs that he can howl as a wolf.

It is said that this is the version of Link from Ocarina of Time, and Majora's mask, and that he is regretful that he did not teach and pass on these lessons that he learned to people who would come and ask for them after he went back to his childhood, this version of Link wants to make sure he does pass something on and ease his regrets, and so he teaching seven skills to his descendant, who is the Link of Twilight Princess.

Source.