The Low and High gain settings are simply 6dB apart. 6dB means 2 times amplification. However, this also means 2 times amplification of noise. The difference is not so much, so the noise floor will not be very noticeable unless you are very fussy. However, 2 times the voltage means you can drive harder to drive headphones.
There is, theoretically, no reason to not keep the player on low gain and raise the volume as needed, as long as the maximum volume is sufficient. If the volume is not enough, then high gain can solve the problem.
However, using high gain with low volumes does 2 bad things: amplifies the inherent noise floor and also exposes the output signal to corruption of silence bits or soft sounds, since the dynamic range is less than normal for the respective noise floor (which does not change with volume settings, since it is not an input signal, but a characteristic of the output stage of the amplifiers).