Kohaku is a rather accident-prone angel who has come to Earth in search of her mentor, Hisui. When she gets trapped in a tree and attacked by a crow, she is rescued by Shuichirou, a young doctor. As a result, she feels indebted to grant him one wish but finds the kind doctor is satisfied with all aspects of his life. Thus, she remains with Shuichirou in hopes of repaying him somehow (subsequently getting in other sticky situations as a result).
Kohaku is neither boy or girl. Stuck in like a like a neutral gender seance he/she is an angel, but is more refereed to as a girl because of her more feminine personalty.
Wish spoilers
After Shuichirou's sudden death, Kohaku is put into a hundred years sleep, so that Shuichiro will have been reincarnated by the time Kohaku awakens. One hundred years later, the reincarnation of Shuichiro, now 17, passes by his old house which awakens Kohaku. He has no memory of her, so their relationship starts anew.
Kobato spoilers
Kohaku is an acquaintance of Genko and several of the inhabitants of the Spirit World, many who admire the angel's singing voice, and has commented on Kobato's progress and the consequences of Ioryogi's actions. After meeting the angel, Ginsei begins visiting Kohaku on a regular basis, particularly as he begins to worry about Kobato and Ioryogi's fates if Kobato is unable to fulfill her wish.
In the manga's epilogue, Kobato and Kohaku meets for the first time in Genko's shop and sing a song together in front of Ginsei.
She lives with the current reincarnation of Shuichirou and tries to help him in every way she can.
In the anime series, Kohaku is introduced early in the series and befriends Kobato. Because Ioryogi is aware of Kohaku's true nature, he constantly asks Kohaku if there's something they can do to change Kobato's wish, though Kohaku's response is always that there's nothing to do. At the end of the series, it is Kohaku who explains to Fujimoto the nature of Kobato's wish and assures the young man that if they are fated to be together they will be in time.
Drug&Drop spoilers
She appears in the latest chapters of Drug&Drop. Kazahaya goes to Shuichirou's house for an errand and his presence wakes Kohaku from her sleep. They quickly become friends and promise to meet again. Although it's not confirmed that they're related, Kazahaya and Shuichirou share the same surname.