What does the audio term 'air' mean?

When talking about black backgrounds, this comes mostly from the electronics, black backgrounds are the result of lowered noise floor which results in higher resolution/transparency. With lowered noise floors we hear far more of the 'inner' details, it is generally these 'fine' details which heighten the sense of spaciousness/air. Source extracts it from recording, pre/amps job to not lose any of that info, speaker reproduces it accurately, room allows speaker to reach full potential. In the final analysis it is not the speaker that produces air/spaciousness, the speaker can only reproduce what it's fed, some have greater potential to maximize what rest of system feeds it. SNS

I have no idea if my electronics produce a black background with a lowered noise floor. Even when I turn on my tubed phono preamp my speakers sound dead quiet. When I stream music I hear no background noise. Of course, when I play a record there is always some source noise even on my quietest records. And yet to my ears, records have more air than streaming does. I can hear more deeply into the music. The instruments sound more present and true to life. I guess that is a good part of what I think of as air.

I have listened and compared very good speakers with the same front-end electronics and one sounds like it has more air than the other. Not because one provides more inner detail, but I would say that one is more analytical and the other more musical. For example, I think my Sonus Fabers tend toward the musical end of the spectrum and Dynaudio or Vienna Acoustics more toward the analytical. And I can totally understand why someone would prefer Dynaudio and Vienna Acoustics over Sonus Faber. Yet audiophiles seem to drift one way or the other.

Another example, before Krell was off the market I really didn't like it. A friend let me borrow his Krell 250 while he was on vacation and I put it in the place of my McCormack DNA-1. The Krell had stronger bass and I think more definition. But I felt the McCormack was much more musical and the Krell was dry. Yet many people swore by Krell. 

There is something going on that I can't put my finger on, but I do think audiophiles tend toward one end of the spectrum or the other. Musical versus analytical? Air versus exactness? I don't know how to define it. 

smooth upper frequency extension with the ability to clearly sound out delicate hi freq details with respect to a wide and deep soundstage

Cey, I think you are right about smooth upper frequency extension, but I think there is something also to the way the musical notes sound on both uppers and mids. I'm not sure about bass. People love tube gear because it brings "bloom" to the sound, which to me means that the notes are voluptuous, as opposed to lean. (Sorry about the metaphors, but I can't find other words.)

In a way, the notes have inner air, and bass notes count too, I guess. I think of a jazz bass where the notes seem to float on air as opposed to cutting the air. So hard to explain. Perhaps a system with air embraces the listener rather than impresses the listener with its strength. 

I'm trying to compare very good systems in my mind. A Wilson speaker or Dytnaudio speaker which I think of as more lean and analytical versus Sonus Faber or other speakers that people think of as "musical." They both could have "smooth upper frequency extension," but one would seem to float on air and the other to penetrate the air. And that's the best I can do at describing what I think I am talking about.

Low noise floor is an electronic design concept...

We can improve it in a various way by filtering DC for example..

By grounding our pieces of gear ....

by protecting it from EMI interference...

"Air" between notes and instrument is the fluid quality, a respiration, uniting but  separating the instruments and the music  as an organized perceived whole by the listener...

A better grounding of the gear pieces for example can increase the perception of "air" between instruments already in the recording because of a lower noise floor...

But acoustics control of the speakers/ room  pressure zones distribution can contribute to the spatial perceived attributes of sound as it must be translated optimally for my ears in my room ...

When listening to an opera in my room if i perceive the singing actors walking and if i see them when singing turning their head it is because the original recording acoustics is well translated in my own room acoustics parameters there is "air" between the singers and the instruments, a space of their own but linked to the others, because they were recorded in the same room now transported in my room  and perceived  as if i was there....

I agree with what most have said. Generally, an open high end that doesn't sound muffled or rolled off at all. 

My ears only hear up to about 12.5KHz now, but even I can hear "air".  I notice it very much when comparing concert recordings done with decent microphones and preamps versus great microphones and preamps. 

The ones done with better equipment sound more transparent and open - more "real", especially upon close listening with good headphones. You feel like you are in the room and not listening through a microphone. It is difficult to describe, but it is like a thin sheet is taken away from your speakers and you can better hear everything. Whether that is "air" I'm not sure, but it is to me.