She's the princess of the alien race, the Karastengu (Crow Goblins).
Like the Oni, Tengu are yet another mythological Japanese creature turned
alien. Karastengu are a type of tengu with distinctly crow-like
features.
The royal line was fading away since there were no more humanoid
men on her planet. To save the Kurama line she had been placed
in cryogenic sleep. While she slept, her little crow subjects
were to search for a handsome and virtuous man who would wake
her from her sleep and become her mate. By Karastengu law she
would mate with the man who woke her up from her slumber
with his kiss.
But because of an unfortunate turn of events, the man who gave her
a wake-up kiss was none other than Ataru Moroboshi. This wasn't
the man she wanted. Ataru who severely repulses Kurama was by no
definition a virtuous man.
Initially Kurama thought she might be able to reform him, but after
every attempt failed, she saw that he was truly corrupt to the core.
Now she's just trying to avoid having to mate with him. To remedy
this she tries everything to land herself another man, preferably
with more looks and less stupidity, but she has had no luck. There is always
one flaw that ruins it for her. Mendou turned out to be too pathetic and
cowardly, Ryuunosuke wasn't really a man like she thought, and Rei seemed like the
one until she saw he was really an idiotic tiger-cow. There seem to be
no good men left for her and now she's become bitter and needy.
Kurama's mind is set completely on saving her bloodline. Because of
this all-consuming drive she's usually a mean person towards others.
She has an especially profound dislike of Oni. Kurama's also very
superficial, she only shows interest in exceptionally handsome men.
Her alien power is her ability to create powerful gusts of wind with
her multi-use giant leaf. (To my knowledge these leaves are a trait of the mythological
tengu).