Narrative is an undeniably important part of any modern game. While it is ultimately not crucial to the game's success *cough Team Fortress 2 cough*, it IS important regardless. Personally, I rarely play a game unless it has a story that seems like it's worth delving into. When I first heard about BioShock, I was admittedly skeptic about it. But after awhile, I decided to give it a try, and I enjoyed the experience.
Keep in mind - There are no "cut-scenes," per se. Instead, the entire game is seen through Jack's -the main character/the player's character- eyes. This helps draw the player into the story being presented to them.
BioShock starts off with a plane crash in the middle of the Atlantic Ocean, and your character is the only survivor. However, there is a lighthouse less than 100 meters away from the crash, and after you make your way over to it, there is a bathysphere (this -->) inside. The player enters it, and it begins its descent into the abyss.
On the way down, an old film reel kicks up. A few moments later, a picture of a man appears, and introduces himself as Andrew Ryan. After speaking for a minute, the player sees a vast underwater city: Rapture, Ryan's escape from society. Ryan disagreed with capitalism, communism, and most other forms of government, so he recruited the top scientists, artists and industrialists from around the world and built an hidden utopia. But moments after the ride ends, it is quite apparent that all is not well within the city. The player has a front row seat to a man getting brutally murdered. After the gruesome scene concludes, the nearby radio goes off, and tells the player to leave the area and get to higher ground. Jack makes his way to a vending machine of sorts, and injects himself with a vial of goo, which "re-writes his genetic code." This process knock the player out for a good period of time.
This constitutes the first ten minutes or so of the game, and it already tells a good chunk of the story. The player has to survive in an unknown environment with apparently hostile natives, who have all probably injected themselves with the magic-do-anything-juice, or plasmids, whichever you prefer. As the player progresses through Rapture, they discover what transpired to bring the city to its current state (SPOILERS: ADAM, the fuel source for plasmids, is largely to blame). The game also leave little tape recorders along the way for the player to pick up and listen to. These are completely optional, and do not impact gameplay at all, but for those of you who are curious about somethings story, they give hints and unique perspectives about the city and its residents.
BioShock shows that narrative in games does not have to be cut-and-dry, go here, shoot this, investigate that, here is your ultimate objective, go complete it. In fact, BioShock is a game that forces the player to work off of little-to-no information, which at times may seem frustrating, but in reality is the green light to go out and explore the technological masterpiece that is Rapture.