Yomi is a demon with six ears and long, black hair. A long time ago, he used to run with Youko Kurama's thieving band. Yomi always wanted to be leader of his own kingdom one day, and he wasn't satisfied in taking Kurama's orders. Many times, he would lead a band of his own off on a raid and be responsible for many losses within Kurama's subordinates, because he had a very self-righteous attitude.
Then one day, Yomi gathered a group of thieves again for a raid, but it soon turned into a major ambush... all planned out by Youko Kurama himself. All of Yomi's men were killed, and the assassin managed to slash Yomi's eyes with his swords. Yomi acted bravely, however, and fought back, warding away the assassin. But he remained permanently blinded ever since.
Centuries passed, and Yomi was soon a leader of his own kingdom in Makai, called Gandara. He was one of the three great leaders of Makai (along with Raizen and Mukuro), and was generally respected by everyone. This was taking place along the times that Hiei and Kurama were invited to Makai. Kurama, of course, was invited by Yomi; however, Kurama was not as powerful as he used to be, and he knew he would be at the mercy of Yomi and his requests.
Yomi decided to spare Kurama's life (and family) in exchange for his assistance. Yomi needed to pull together a team for the Makai Tournament that was going to be held (by Yusuke), and he figured that Kurama would be a helpful ally in that condition.
Another big part of Yomi's life is Shura. Shura is his son, born from an artificial womb and is equal in strength to Yusuke. In an unfortunate turn of events, Yomi is paired to fight against his son and wins, as expected.
A big part in Yomi's appearance in the anime is the fight between Kurama and Shigure. Yomi is desperately hoping that Kurama will revert back to his Youko form to win, but Kurama instead decides to leave the past behind. Yomi also decides to respect his decision, and helps Kurama off the battlefield when the fight is over.
Soon after that fight, Yomi faces off in a fight against Yusuke, Raizen's apprentice. In a fierce battle, Yomi wins by a thread. He then quits the tournament afterwards, handing the win over to Enki (another demon).
At the end of the Makai Tournament, Yomi and Kurama meet again. Despite the tense moments between the two, Yomi tells Kurama that he was happy to see him again. He then walks away, starting a journey with Shura with the purpose of preparing him for the next big tournament. That's the last we see of Yomi and Shura in the anime series.