[merylsilverburg]

Digi basically explained it pretty well, but just in case, I decided to put in the story lines and all that I got from a chart in an OPM magazine.

OPM: Issue 60, September 2002
Tekken
The worldwide martial arts tournament funded by the Mishima Zaibatsu corportation is nearing an end. Only eight fighters remain. The remaining fighter will take on Heihachi Mishima for a chance to win a large cash prize and be crowned The King of Iron Fist.
Kazuya earns the right to face his father, Heihachi, at the end of the tournament. The final battle takes place at the same spot where Heihachi had once taken down Kazuya at the age of five. This time, Kazuya emerges victorious, bearing a scar across his chest from his father. Kazuya then tosses Heihachi's body off the edge of a cliff. Once done, Kazuya gains control of the Mishima Zaibatsu and takes the corporation to new heights.

Tekken 2
Two years after the conclusion of the first Tekken, someone within Mishima Zaibatsu mysteriously notifies news agencies around the world about a new tournament with a prize worth over a thousand times more than the first tourney. So begins Tekken 2.
Jun Kazama learns that the source of Kazuya Mishima's power is his Devil Gene- yet she's still drawn to him. Similar to the first tourney, the second Tekken ends with a final match between Kazuya and the mysterious organizer of the tournament, Heihachi Mishima, who everyone thought was dead. This time, though, Heihachi wins. Unaware of the Devil Gene within Kazuya, Heihachi casts his body into a volcano and regains control of the Mishima Zaibatsu. With Kazuya gone, Jun hides and raises their son, Jin, on her own.

Tekken 3
Fifteen years later, martial artists around the world are disappearing without a trace. Sensing that an evil darkness is upon her, Jun tells Jin, now a teenager, everything about his family's haunted past. She also tells him to seek out his grandfather, Heihachi, if anything should happen to her.
One night, Jun's premonitions come true when she's attacked by Toshin. Jin tries to protect her but is knocked out during the fight. When he awakens, Jun and Toshin are gone. Knowing his mother has been slain by Toshin, Jin goes to Heihachi so he can be trained and get his revenge.
To draw Toshin out, Heihachi sets up a third tournament. Four years after Jun was killed, Jin, now 19, defeats Toshin, but Heihachi betrays Jin by mortally wounding him. With his life fading, Jin transforms into a Devil and strikes down Heihachi before disappearing.

Tekken 4
Having failed to capture Toshin for genetic experimentation, Heihachi orders his scientists to gather tissue and genetic samples in hopes that he can splice Toshin's genetic code with his own. Heihachi soon discovers that he needs the Devil Gene to carry out his experiment. Since he lacks this gene, he seeks out the one person who has it- Jin Kazama- but comes up empty-handed.
Heihachi soon learns that rival company G Corporation has unearthed Kazuya's body. Knowing that Kazuya also had the Devil Gene, he seeks to steal the body. His task force makes a hit on the company, but they're taken down by a lone figure that Heihachi learns is Kazuya. Kazuya had been resurrected by G Corporation, which is helping him understand and control his Devil side.
In order to capture Kazuya, the Mishima Zaibatsu announces a fourth tournament, only two years after Tekken 3. The challenger who defeats Heihachi would win control of the Mishima Zaibatsu. Knowing that this was a trap, Kazuya enters, still thinking that this is his best chance to defeat Heihachi once and for all. And so, the fourth tournament begins.

There's also a character relations chart in this issue, but I don't know if anyone wants to read about that. I hope this helped.