If this just a normal FPS set in a decaying urban environment, then it's graphics alone would make it brilliant. When I first played it, I kept waiting for the FMV cutscene to end, before I suddenly realised I was looking at in-game graphics!
But it's not just a normal FPS. The designers have added layer after layer of additional good stuff that make's it so much greater than the sum of it's parts. Here's a few:
The setting and story - the jaunty but decayed art deco city of Rapture is a beautiful thing to behold and, much like the classic 'Resident Evil' games, clues you can collect throughout the game allow you to piece together the city's short and troubled history. There's a great twist in the story with a 'Usual Suspects'-style reveal which will leave you thinking "How come I didn't notice that before?".
Weapon upgrades - As well as the usual rack of weapons, you are given the chance to create a customised arsenal by using the limited number upgrade machines to increase the killing power of your weapons, be it reducing the recoil of the Thompson or adding a 24-round autoloader to your six-shooter.
Plasmids - these are the genetic power-ups discovered by Rapture's scientists. Some you will have to pick up, but others can only be aquired by entering secret areas or by using your camera to research your enemies. There are different types of plasmid too, ranging from offensive ones such as Incinerate to passive ones such as the one which makes you invisible when standing still (great for sneaking up on enemies). The Adam used to buy plasmids also leads to the game's important moral decision for the player - to save or damn the Little Sisters.
Hacking - Rapture is littered with autodefenses such as security cameras (which unleash security bots), machine gun turrets and rocket turrets. The game allows you to use a puzzle-based system to hack into these elements and turn them into your allies. So, whilst you're all alone in Rapture, you don't necessarily have to be without backup. The hacking system can also be used to reduce the cost of supplies and unlock new ones.
Atmosphere - the makers of 'Bioshock' have gone to great lengths to increase the fear factor of the game. They've done this through intelligent use of light and sound; meaning that you'll see the shadow of some terrifying new enemy before you see the enemy itself or you'll hear there footsteps or demented singing (I never knew how scary the words "Jesus loves me, this I know..." could be).
Taken separately, all these elements would be good. Put together they make one of the best games I've played in a long time.