Mukuro is one of the Three Kings of Makai. She's been a sex slave since birth and on her 7th birthday she decided to pour acid on her body to have her master abandon her. Once free, she replaced the burned right side of her body with mechanical parts and masked herself to hide her womanly status. In the following centuries, she became more and more strong, feeding her powers with the hate derived from her traumatic childhood, and slowly built a kingdom until she became strong enough to face the Makai Lord Raizen and started a war against him.
She was saved to be consumed by hatred by finding Hiei's lost Hirui stone, that had the power to calm her soul, and later she summoned Hiei to be her ally in the Three Kings war, and she developed a deep bond with him due to them having both experienced deep hate and traumatic childhood.
During the Makai tournament in the anime, she fought Hiei and she won, but he managed to break the hard chains that she had on her wrists since the time of her slavery, a symbolic way to free her from her past. In the manga, Hiei does the same thing by capturing her abusive master and removing a mental conditioning that prevented her from trying to kill him.