The game is set in 1912 and based on the floating city in the sky, Columbia, where you assume the role of Booker DeWitt, a disgraced Pinkerton agent. You have been given the job of finding a woman named Elizabeth in Columbia.
Like in previous BioShock games, you will possess extraordinary powers such as Telekinesis and Electro Bolt, but it is unknown if these powers come from plasmids or if they lead to the invention of plasmids somehow. Elizabeth also possesses powers which will often be used in tandem with yours to make attacks more effective. An example is where Elizabeth creates a rain cloud and you use a lightning attack.
Source: Big Download