Hero's Spirit

In Twilight Princess, the Hero's Spirit, also known as Hero's Shade, is an undead specter that taught Link each of the seven Hidden Skills throughout the game. The Hero's Spirit is also believed by some to be the spirit of Link from Ocarina of Time.

The Golden Wolf
The Golden Wolf, also called the White Wolf, is the animal incarnation of the Hero's Spirit. The wolf is summoned by finding a Howling Stone, with the exception of the first time, in which he confronts Link directly. Once a howling stone is found, the song has to be howled in tune with the Spirit. He then tells Link to take "sword in hand" and find him, implying that Link had to return to human form before searching for the Wolf. Once Link encounters the Hero's Spirit, the Golden Wolf will appear as a symbol on Link's map. When he confronts the Wolf, Link is transported into an ancient arena. The wolf then finally transforms into his true form, the Hero's Spirit, who then teaches the young hero one of the seven hidden skills. The true form of the Hero's Spirit resembles the spirits in Hyrule Castle's graveyard.

Hero's Lineage Theory
Although they are not conclusive, and easy to interpret as mere simularities, there are several indications that the Hero's Spirit could be an ancestor of Twilight Princess ' 's Link, or even the Hero of Time himself.

The Hero's Spirit claims that in the past, he was a hero, and most of the songs that activate the Howling Stones are from Ocarina of Time or Majora's Mask, although the "Ballad of Gales" from The Wind Waker also appears. Like Link and several others, he wields his sword in his left hand, and it has faint similarities to the Master Sword, while his shield somewhat resembles Termina's Mirror Shield.

At various points, the Hero's Spirit commands Link to, "Go and do not falter, my child," and explains that the skills he is teaching Link "do not leave our bloodline". However, it is possible he was simply referring to the bloodline of the Knights of Hyrule, rather than one specific to Link himself.

Trivia

 * The first song that Link howls in order to begin the quest of easing the Hero's Spirit's regrets is the Song of Healing.
 * Once Link learns the final Hidden Skill, the screen goes white and the Hero's Shade speaks his final sentence, "Go, and do not falter, my child!". This is similar to how the Seven Sages from Ocarina of Time speak their final words to Link.