The Devil Gene is a genetic abnormality found within some members of the Mishima bloodline.
Originally, Kazuya Mishima sold his soul to the Devil in order to gain the power to defeat his father, Heihachi Mishima. This imbued him with the Devil Gene, which allows him to transform into a powerful demonic form with wings and a tail. This gene was seemingly passed on genetically to his child Jin Kazama. It should be noted, that while Jinpachi Mishima--Kazuya's grandfather--also has the power to tranform into a demonic form, it is not cause by the Devil Gene, but something else. Also, Heihachi shows no sign of having the Devil Gene either, but rather aims to take it from Kazuya and/or Jin to use it for himself.