Haku is a white dragon who befriends the main character, Sen/Chihiro, and eventually aids in her escape from Yubaba’s bath house. He is able to turn into a human at will, as well as cast spells of unbinding, invisibility, and binding. Haku is the spirit of the Kohaku river, which a young Chihiro fell into as a child. Since then, the river has been paved over.

In smaller pieces of anime by the author concerning Spirited Away, it has been assumed that Chihiro’s mother and father despised the river, for almost killing their daughter.

Since in Japanese mythology the health of a spirit is connected to the natural feature such as a mountain or stream they inhabit, it can be assumed that the destruction of his river is what drove Haku into Yubaba’s servitude, hoping to gain greater power. His love for Chihiro is eventually, what led Yubaba to eventually release him, as, because of the shared love of Chihiro and Haku, they finally learned their names.

Trivia:
In the japanese version, Haku’s real name is given as Kohakunushi Nigihayami, or Nigihayami Kohaku Nushi, instead of the simpler Kohaku River name given in the English dub. This minor difference is one of the reasons the dub version is panned by a lot of fans.
Haku can be translated as “white” in Japanese, refering to his white color.

text taken from wikipedia