Kazuya Mishima is the son of Heihachi Mishima (see Part 3) and father of Jin Kazama. Kazuya entered the first Tekken tournament to challenge his own father. He defeated Heihachi and threw him off of a cliff in a failed attempt at patricide. Kazuya then took over the family business, the Mishima Zaibatsu, only to become more corrupt than his father ever was. This was due to a Devil Gene controlling him, a result of Kazuya essentially selling his soul while succumbing to hatred for his father.
After Tekken 2, Heihachi gets revenge by tossing Kazuya into a volcano. The G Corporation recovers and regenerates Kazuya's remains in order to perform research on his Devil Gene. Through this research, Kazuya eventually learns to control the Devil Gene and activate its transformative powers at will. After some time, Kazuya rises to control of the G Corporation and uses it to battle the Mishima Zaibatsu, which is now run by his son Jin.
Kazuya, like his father and son, practices Mishima-style Fighting Karate. The Mishima characters all share a very similar moveset, though it has become increasingly differentiated with time. The situation is very similar to the "shotos" Ryu and Ken in the Street Fighter series. The signature moves of this style include the Wind Godfist and Thunder Godfist.
Wind Godfist and Thunder Godfist are both performed with a shoryuken-type motion, albeit with separate punch buttons. Rising Uppercut is the right-punch version and functions as a launcher. Dragon Uppercut is the left-punch version and is basically Tekken's shoryuken. It has a forward-stepping crouch that leads into the rising punch that can be used to advance under attacks and counter them. It also knocks the opponent down in most cases, which actually inhibits its use, as it cannot be used to launch or start combos.
There is a variation of the Wind Godfist called the Electric Wind Godfist (EWGF) that is superior in every way to the original. The catch is that it is more difficult to perform due to a very narrow input window. The EWGF is an electrified version of the Wind Godfist that has faster startup and recovery, gives frame advantage on block, has a bigger hitbox, and does more damage. It is arguably the best launcher in all of Tekken, and it is a prerequisite skill for any Mishima player to have.
Kazuya's style of play seems to center mostly around counter attacks. The Kazuya player will focus on baiting the opponent into an attack and punishing with a move like EWGF. From there, he gets a launch into a damaging combo. In the Street Fighter X Tekken gameplay demo, we see Kazuya doing this by ducking through fireballs or backdashing through normals before punishing with a combo ending in a knockdown. His style should translate well to the new game, without making him play exactly like a projectile-deprived Ryu.
(Source of story background and moveset info: Tekkenpedia)