Basically you are this guy and you survive a plane crash, in the water you come across this building once you enter a chamber you find your self going below the water to a city named Rapture, however you soon find out with the help of your guide Atlas that things are not all that they should be.
But trust me thats just the beginning.
Well you play as jack soon you find the inhabitants of Rapture have gone mad, and have been twisted and deformed by ADAM, at the beginning of the game you obtain some ADAM, which is a parasite that attaches to the hosts cells and changes them, which gives you some great powers, such as Electro ball, Incineration, and Telekinesis (there the only ones I have so far) however you need EVE to replenish the use of your power, the inhabitants are all after ADAM and have become twisted and deformed; crazy (a thuggish splicer singing, rock a bye baby with the pram containing only a revolver)
However soon you encounter a bigger threat.
The splicers as they are called kill each other, soon Little Sisters appear and harvest blood with a needle to reuse the ADAM, Little Sisters are guarded by the giant BIG DADDY'S, and they are as Hard as hell, protecting the sisters and killing you quick, most of the time inhabitants will try and destroy a Big daddy, then turn on you (like usual) however Rapture is sinking and the villainous Ryan has made sure escape is impossible almost, if you defeat a Big Daddy you can either Harvest a little sister or take.