This game is in fact a story first and a game second. The average first person action facade is simply there to focus the overall purpose of the game, to explore the darkest area of mans mind. How far will one go for power?
The setting of this question is set beneath the sea in a city named Rapture. The godless city was founded by one Andrew Ryan. A man with a vision of a city with complete artistic and scientific freedom. This vision manifests its self in an unexpected way. The inhabitants of Rapture effectively rip the city apart from the inside out, leaving it a dark wet hell with monstrously deformed humans roaming its interior. It is in this hell that the player will fight for survival against Rapture and its unlawful ways.
Technically this game is nothing to gawk at. It would seem just another graphically driven first-person shooter. It's game play is not particularly deep and the level design is fairly linear. There is no attempt at multiplayer or even leader-boards. It is a simple first person shooter with a variant of spell casting.
So what deems this game not a throw away? The story.
The setting is unique and fascinating and filled with detail that brings this horrific place to life. The script for the game is written with incredible insight into human nature, as well as, the occasional stunningly bizarre monologue. The voice acting is top of the line. Not one character in the game sounds false. They drag you down to this murky world and you find it incredibly easy to empathize with each and every character as the game progresses. All of these aspects just mentioned are what you play Bioshock for. The story is so finely crafted and executed that this game essentially becomes a page turner. You will simply need to find out what happens next. This games story doesn't let up and it doesn't disappoint.
So, if you are dead set on looking for a game to simply replace your overplayed Oblivion or Call of Duty 4 habits then look elsewhere. But if you are any other sort of creature with a brain. Well... I would say you need to play Bioshock.