I'm completely lost as to the meaning of "grain" in 45 grain brown rice vinegar. What does the grain number mean?
Grain is a measurement of the acidity of the vinegar. It is the acidity percentage multiplied by 10, so 45 grain vinegar would be 4.5% acidity.
Just an addition with some boring math ...
Grain is also a weight unit (64.8mg) based on the average weight of a barley grain. If you add 10 grains (.648g) of barley to a fluid ounce (28.4g) of water and assume that the barley contains 2/3 of fermentable starch (at least close enough for a rough estimate), you will end up with 0.286g of acetic acid dissolved in 28.4g of water if the ethanol and vinegar fermentation completes. This is very close to a 1% solution.
-- converted from the comments regarding the origin of grain: --
It's possible the term 'grain' comes from Malt Vinegar which was traditionally made in England from barley (the grain). The 'grain' number likely referred to amount of grain in the vat of work (water plus grain) which resulted in higher acidity.
Acetic acid (main acid in vinegar) is produced by fermentation of ethanol which is produced by fermentation of starch/sugars which is the starting point of the process.
Therefore the maximum acidity of a given batch is predetermined by the starting amount of sugar/starch in the grain. And if the grain is uniform, it can be used as a unit.