The way I always thought about it (whether or not it's correct is another question), is that the offset subtracts (or adds) a dc level to the signal such that if you switch to high current, you adjust the offset to cut out a lot of the input signal that is just squeezing the contrast you want to see into the upper end of the range. Then adjust brightness and contrast to effectively stretch (linear amplification) the visible signal to cover the dynamic range of the display.