A lifetime ago, Kurama was the leader of a group of thieves. His second in command was Yomi, who would later become one of the three most powerful demons [youkai] in Demon World [Makai]. But Yomi was a ruthless and brainless fighter who didn't want to listen to the much smarter Kurama. When Yomi ran his own group of thieves and let many loyal followers die by acting on instinct instead of thoughts, Kurama sent an assassin to kill him. This assassin failed, however, and only ended up blinding him. The assassin would wind up regretting this, as the powerful Yomi tortured him until the day he died.
But then, when he was chased by a Spirit World [Rei-kai] bounty hunter and got injured, Kurama (in his fox form) fled to the Living World [Ningenkai] and his spirit combined with that of the unborn baby of Shiori Minamino. He was later born as Shuichi Minamino. His human mother loved him with all her heart and taught the once so cold hearted Kurama what human love is. Kurama, who actually wanted to return to Demon World [Makai] as soon as he regained his powers, learned how to love and to care and found himself unable to leave his mother. So he stayed to take care of her (he continues to live with his human family today).
Kurama and Hiei met each other when they were in junior high. You may not believe it, but Kurama had short hair! Although Hiei probably will never admit it, they are close friends, know a lot about each other, and even understand each other. When Kurama's mother got sick and could not be treated, he decided to join Hiei and Gouki to steal the three Spirit World [Rei-kai] artifacts to save her life. The item Kurama got was a mirror called the Forlorn Hope, meaning that if the person wanted their wish granted, they would have to give up their lives to accomplish this wish, hence the forlorn part of it.
And so he met Yusuke, who saved his life when he wanted to sacrifice his own life to save his mother's. In the end, the mirror granted Kurama's wish and saved his mother's life. He then surrenders to the Spirit World but is later released to join Yusuke's crew (along with Hiei) during the invasion of the Spirit Beasts, maintaining his human form but going by his real name.
Kurama's power is the ability to control plants, especially Makai plants, and his techniques have a uniquely beautiful but deadly quality to them. He always carries a rose in his hair, his means of creating the deadly Rose Whip. With it, he can invoke attacks like the Rose Whiplash or the Thorn Wheel. He's also known to use a Death Plant that can kill an enemy by growing inside them.
Kurama is a very nice person who smiles a lot, but nobody can tell who and what is behind this smiling face. He is an extremely intelligent person, thinks a few steps ahead of normal people, and will never let others know what's on his mind. Even in the most difficult situations, he manages to stay calm and think about the best solution. However, his time as a human has softened what would otherwise have been a very ruthless demon [youkai]...with a reputation feared even today by the demons [youkai] in Hell.
Kurama occasionally returns to his real form, but is basically trapped in his human body and can only come out with special items like the Idunn Box or with the Fruit of Past Lives. In his real form, Kurama's power of plants increases significantly, and the white clothes of his real form are created of demon substance and they have defensive powers like those of Sensui. Also, he regains his cold bloodedness from before his life in the human world.
In his past, Kurama's closest friend and companion was Kuronue, who died during one of their robberies in Demon World [Makai]. Kurama is still quite upset about his best friend's death, the feeling which the enemies of the second Yu Yu Hakusho movie took advantage of.