As in does does voltage correlate to decibels or tone or anything like that?
The voltage corresponds to the instantaneous sound pressure of the air. It change all the time from a positive value to a negative value. The peak voltage has some relationship with the loudness of the sound but not direct. The time it takes for the voltage to go from a positive peak to a negative peak and back again is related to the frequency.
and how exactly I would get the music from the computer to the Arduino.
This shows you how to get the audio signal into an arduino:-
http://interface.khm.de/index.php/labor/experimente/arduino-realtime-audio-processing/
However, as I said YOU need to do a lot more research on what an audio signal actually is.