The question in my mind is this... does it imply that it keeps what's below that?
Not neccessarily..
It seems the encoder you are using low passes the signal first before doing any other processing, and that low pass filter has a
transition band between 19383 - 19916Hz.
The
transition band is the sloped part of the frequency range beween the
corner frequency (which is where the filter starts working) and the
stop band (which is were the cut-off is essentially complete).
That part is pretty simple in audio terms.
The complicated part is all the stuff that happens after that. MP3 and other lossy compression formats use
perceptual encoding which means that the information they choose to discard after that simple low pass filter are things that the codec creators have decided humans don't hear well. There lies the fuzzy art of perceptual encoding. It does more than this but as an example: if there is a quiet sound that happens simultaneously with a loud sound, then the loud sound will tend to mask the quiet sound, so the quiet sound is thrown away.. hopefully without a human noticing. MP3 is specifically tailored to the way humans hear. It may not work as well for other animals.
So it does not keep everything below the low pass frquency, but is clever about what it decides to discard.
I'm sure there are much better descriptions of how the process works, but at least that should give you a basic idea of part of what is going on.