Tony is a billionaire because he is the head of Stark Industries, a company primarily concerned with making weapons for the military, which of course allows him to become a superhero in his off hours.
The Big Twist:
Tony thinks he's going to spend his superhero time Iron Manning terrorists to death, but the surprise twist is that his true enemy is someone close to him. His lifelong friend and mentor, Obadiah Stane, has been secretly selling weapons to terrorists, because there's apparently more money in that. He is, in fact, the one who originally set Tony up to be captured at the start of the movie.
"I see no way that not deleting this video can come back to haunt me."
After his plan to have Tony killed fails, Obadiah makes a move to take control of the company by filing an injunction against Stark with their board of directors behind his back, a fact he shockingly reveals to Tony at some weird tuxedoed science fair.
But How Did He Not See This Coming?
Hold on just a damned second. Tony isn't an entry-level worker or mid-level manager at Stark Industries. He is the fucking CEO. His name is on the goddamned building. Why the hell didn't one of his 7 billion phones and/or answering services ring the instant the injunction was filed? Why didn't Pepper, Tony's personal assistant who handles every single aspect of his life, pass on the information?
Her punishment? She's named CEO in the next film.