Better to think of it as dimensionless. It is just a virtual value, a digital number, until it touches the outside world.
Well, it was once touching the outside world -- if it was recorded -- but without knowing the calibration of that microphone, that's pretty much useless.
For almost all purposes, just appreciate that the components that make up, say, a song, are layered in just the right amount to sound good. The frequency response, reverb, distortion, volume, compression, stereo balance and phase, etc. are all adjusted in mastering.
So, who knows about calibration, in most cases.
Once it leaves the sound card's DAC, however, it becomes referenced to a real unit of measure. The reference voltage of that DAC is one unit, and the value the DAC is set to, is some fraction of that unit. That gives us a reasonable calibration point to reason with.
It may also help to understand fixed point. When you write out a number 1234.5678, the 1234 part is the integer part, and the 0.5678 is the fractional part. We can compose such a number by starting with an integer (12345678), and shifting it right (shifting the decimal left), which is equivalent to multiplying or dividing by (base)^(shifts), in this case 10^4.
In the same way, we can store a binary number as raw packed bits (in this case, 16-bit words), and read them as any representation we like. In particular, if we read them as all-fractional (a 0.16 fixed point format), then we also have the representation used by the DAC -- a fraction of the total VREF.

By the way, if you're familiar with U.S. customary length measurements (inches and fractions), you already know binary fractions. For each 1 in the fraction, move to the next tick mark on the ruler, where the height of the mark corresponds to the position of the digit. So, 0.111b means, take 1/2, and 1/4, and 1/8 = 7/8 total. 0.1b is 1/2, 0.101 is 1/8 more than 1/2 = 5/8, etc.
Every so often, someone who grew up with Good Old Boys (aka rednecks) then learned a computer trade, realizes Bubba invented this system independently, by -- instead of calling out the total fraction, because that's hard, who wants to add and reduce fractions? -- just calling out the number of tick marks from biggest to smallest.
Or to put it still another way -- take the count (-20k to +20k or so), and divide by 32768. Reduce the fraction if you like, but suffice it to say, it's the long-hand way for the same method and answer.

Tim