"You could never find a use for a picture from NASA's site" says no one ever.
So how do we define the atmosphere? In the vaguest of terms, it's everything added to the base outline of a game. These are things that you usually don't interact with directly, the music, lighting, wall decorations, and in Bioshock's case, the Audio Recordings. The cumulative effect of all these things can have a profound effect on the way you experience a game. Hell, the random spots of old-timey music you hear while you explore the city of Rapture just adds to it. When the game can make it's own mythology and setting feel alive, that's when you have good atmosphere.
We never talk about the atmosphere of really any genre besides ones that have either a gritty feel, or ones that have traces of the horror genre. It can be hard to call a game like Psychonauts "atmospheric", even though it does a lot of the same things. The music, setting, and imagery is all consistent with what the game sets out to be, but it doesn't carry the same weight as the world in Bioshock.
Brain Diving Catan! I would play an expansion like this.
I think this issue may come from the fact that people started using "atmosphere" as a way to define horror games. They wanted a word to explain a feeling of tension. Look back at Resident Evil 1. The game was really bad in terms of controls, but everything about it was tense. Look at Silent Hill 2, a game almost universally praised. The fog added uncertainty, and made you paranoid.
Looking at this, we can redefine atmosphere as such: The feeling of "what the hell is going on here?".
Sure, games have uncertainty in them. If they were predictable, you wouldn't want to play them. games that have great atmosphere though, they affect you at a deeper level. It becomes a morbid curiosity. You want to know more about what's going on, but you're apprehensive about what's coming up next. When you're in this state, everything becomes more effective.
Now there's one other game I want to mention (again).
No! Not you!
The game is Vampires: The Masquerade Bloodlines. I touched on this before in my last post, but I felt like it needed repeating here. I think what helps draw me into it, personally, is the minimalistic background music when you're not in nightclubs, or around radios. It's very simple, but haunting enough to keep you focused. This game is like Bioshock in that it makes it's own world feel alive, in a sense. You hear a radio DJ taking phone calls at night and you can read random emails that have no bearing on nothing whatsoever, but these things are important for world building, which, in turn, sucks you into that world.
So, those are my thoughts on atmosphere in gaming. I think the term gets used loosely a bit too much. I feel like it's more akin to tension, but what do I know? I just write on a random blog for fun. Feel free to make your own interpretations of the word.