Shinji is basically the guy who shares Sosuke's obsession with Arm Slaves—easily his closest friend at school besides Kaname. His passion for AS runs just as deep, which is probably why they click so well.
His interest in mechs comes from his dad, Shintaro Kazama, who's a secretary for Narashino's Assault Machine Troop. The thing is, his father failed to become an AS pilot, and that failure stuck with Shinji. He's been driven ever since to figure out what went wrong and to finish what his dad couldn't—becoming a pilot himself and fulfilling that dream.
There's not much said about his mother in the series. It's implied that his father was already a widower when the story begins, but the details stay pretty vague.
Content compiled by AnimeList.moe from publicly available sources.