Here's a dictionary.com definition that pertains most to how the word atmosphere is being used in this thread:
3. resembling or suggestive of the atmosphere; having muted tones and softened or indistinct outlines; hazy: atmosphericeffects.
4. having or producing an emotional atmosphere: atmospheric quality; atmospheric lighting.
To me it's just kind of a feeling that you're being taken to another place while listening... You're not imagining a bunch of musicians sitting in separate booths in a recording studio in Seattle when you hear the song. You're taken somewhere. BTCS is to me the prime example of this. Every song has character, tells a different story, paints a very unique and beautiful picture, evokes a different feeling. Nothing on AFTW is very atmospheric for me besides Drunken Soldier, the outro of Snow Outside, and I guess some parts of Gaucho. This isn't to say I don't love the album. I freaking LOVE the album. But as of right now, it's songs aren't as atmospherically transcendent for me as Lillywhite's previous efforts with them. Maybe my feelings will change.
Also, I've heard the If Only and Crush comparisons a few times now and I really, reaaaaaaaallly do not understand it, as much as I want to. If Only is SUCH a dud compared to Crush. I hope in the future, DMB makes some jazzier studio cuts like they did for BTCS. If only doesn't cut it in my book.