Hiei is the son of a Koormine or an ice maiden. Koormine's a race of female who live on a floating ice in Maikai. Because Hiei is a fire and ice demon, Hina has interacted with someone outside the block of ice they lived on, he was thrown off the island with his mother's tear gem. He was taken by bandits, but was forced to leave when they became fearful of him.
Hiei's Jagan eye was implanted by Shigure so he could find his twin sister, Yukina. Although it weakened him, he learned swordsman-ship from Shigure to try to return to his normal strength. He did manage to find her when Botan, Yusuke, and Kuwabara were on a rescue mission to save her. Although she is now safe and a part of his life, he has yet to tell her he is her brother. He didn't want to cause her pain by telling her the brother she seeked was a criminal.
Hiei first meets Yusuke when he kiddnaps Keiko in exchange for rare items. Yusuke does defeat him, with the help of Kurama. To make up for his crimes, Hiei teams with Yusuke, Kuwabara, and Kurama and becomes part of the Reikai Tanteis. Hiei deeply respects his team-mates, even though he doesn't say it (in fact, he doesn't say much). As he continues to work with them, he masters all kinds of techniques and skills to make him stronger. Eventually he will loosen up around them, but it doesn't mean he won't bomb them with insults. He is the least trusted of the group, though, but will always hold his promises.
During the Maikai tournaments, he meets Makuro, ruler of a third of the Maikai lands. Eventually, he becomes her heir, training to become even powerful. He helps her send lost humans that have wandered into the demon world back into Ningenkai.
Weaponry and attacks
Jaou Ensatsu Kokuryuha(Dragon of the Darkness Flames) :: Hiei uses his demon energy(yoki, I believe) to lure a dragon made from yoki flames and send it to distroy his opponent. With the help of his Jagan, he can control it. The first time he used the technique was against Zeru, a flame user, in the Dark Tournaments. His right arm was burned for a while after using it for the first time, because the yoki dragon was somewhat out of control. The second time he used it, however, was against Bui (also in the Dark Tournaments). He found a better way to control it with a dragon tattoo that is concealed by a seal.
Jaou Ensatsu Rengoku Shou(Fist of the Mortal Flame) :: Green flames envelope Hiei's fist and he can hit his opponent multiple times.
Jaou Ensatsu Ken(Sword of the Darkness Flame) :: Hiei summons black flames around his katana and uses his sword like that. He doesn't uses it much, because it's so similar to Kuwabara's Rei Ken. And did we mention he hates Kuwabara as well?
Shadow Sword :: Hiei stole this from Reikai. It has the ability to turn Ningens into demons. The hilt of the sword has a antidote though.
Jagan :: Hiei had this implanted into his forehead by Shigure. It decreases the yoki of the user after is it implanted. The Jagan can see miles upon miles away, so Hiei can find people from far away. It also helped Hiei control his Jaou Ensatsu Kokuryuha.