Heihachi Mishima (roughly translates to "Eighth Peace of the Third Island") is a fictional Japanese character in the Tekken fighting game series. He is one of only four characters (the others being Paul Phoenix, Nina Williams and Yoshimitsu) to have appeared in every game in the series. The official backstory for each game somehow involves Heihachi or his immediate actions, and he makes two appearances within the series as the main antagonist (in both Tekken and Tekken 4), marking him as one of series' central characters.
Heihachi is the son of Jinpachi Mishima, the father of Kazuya Mishima and Lars Alexandersson (though he is unaware of this), the adopted father of Lee Chaolan and the grandfather of Jin Kazama. He fights with the power of Mishima Style Karate and is the founder and the Commander of the Tekken Force Unit. He has hosted all but the second and fifth King of Iron Fist tournaments (which were hosted by Kazuya and Jinpachi, respectively).
Heihachi was born as the heir to the rich, powerful, and well-respected Jinpachi Mishima, the owner of the powerful Mishima Zaibatsu and a world-famous martial arts master. During this time, Heihachi married and eventually had a son of his own, Kazuya. Heihachi raised Kazuya harshly; in his mind, he needed to forge a strong heir to eventually pass the Mishima Zaibatsu to. Much to his chagrin, Kazuya grew up kind and frail. At some point, Heihachi betrayed Jinpachi and stole the Zaibatsu from his father. After assuming control, Heihachi began to steer the Zaibatsu into the military industry while his father vanished. After some time, Jinpachi attempted to retake the Zaibatsu from his son, but he failed and was ultimately imprisoned underneath Hon-Maru, where he would remain for approximately 50 years.
Finally fed up with Kazuya's "weakness", Heihachi tossed his son down a deep ravine, claiming that if he were truly his son, he'd be able to survive the fall and climb back up. Kazuya actually managed to do so, but only because he'd made a deal with the Devil in order to survive. To further motivate Kazuya, Heihachi adopted a Chinese orphan named Lee Chaolan and raised him as a rival to his true son. Over the years, Kazuya traveled abroad and competed in martial arts championships, becoming an undefeated champion (the only blemish on his record being a draw against Paul Phoenix). Eventually, Heihachi decided it was time to test his son's strength, and he announced the King of Iron Fist Tournament.
Much to Heihachi's surprise, he was defeated by his son, Kazuya. Kazuya tossed Heihachi from a cliff just as Heihachi did when he was younger. However, being no ordinary man, Heihachi survived and returned two years later as a competitor in Kazuya's second King of Iron Fist Tournament. After winning the contest, he battles his adopted son Lee and has a showdown with Kazuya and defeats him. Afterwards, he tosses Kazuya into a volcano and shuns his adopted son for betraying him.
(Source: Tekken Wikia)