In 1960, a man named Jack came down to Rapture and did things that would change the city forever. He killed the founder of Rapture, Andrew Ryan, took away the precious ADAM supply by taking the Little Sisters out of the system and then left the city to die. No leadership, no ADAM -- just an ocean of misery.
Ten years later, a new power has taken control of Rapture, Little Sisters have been brought back into the city and new enemies await that Jack wouldn't be able to survive against in this new order of Rapture. Luckily, you're not playing as a regular person. You're a Big Daddy, the first one ever made. Not only are you a Big Daddy, but you're one that has free will, and your actions will change Rapture once again.