It is one of those things I often do unconsciously, especially when it comes to a song that doesn't have lyrics. I hear beats...the highs and the lows. While I may not know the instruments being used I can tell it is there. I can feel what instrument (or sounds) seem to be the main character of the piece and the instruments/sounds that are more of the supporting role.
I can understand what sounds seems to be a wind instrument, or a string instrument. An instrument that gets closer to a trombone or one that is closer to a flute, an instrument that lends itself like a drum (using the hands to create the sound) or one that uses a harmonica. An electronic music that is trying to mimic "x" sound.
The pace of the piece, what sounds are pretty constant throughout the piece? What sounds are pretty irregular?
By the time I go through the list of sounds I hear, the piece is done.
During the whole process, I can also feel what the piece evokes to me. It evokes, happiness, sadness, forgiveness, pain, delight, and everything in between. It is like what people called a "March." It is upbeat, and many different marches tend to put you into action. It speaks... GO!
It is sort of like language, there are nuances (probably big ones) between Spanish, French, and Italian. Just as easily, I can tell the difference between Mandarin, Cantonese, Japanese, Korean, and Vietnamese (could definitely include more into the list.)
I notice the tones, the sounds that are made.
Aside from sidetracking, I was told I can really develop this part of me. Not really sure, I tend to just listen to music and follow the beat(that is, if I actually like the beat in the first place) and notice the sounds within the beat.
Would music theory work? I could just as easily decide to take a language course if it further develops this (I wanted to take a language course anyhow.)