Nihonshudo (日本酒度) is often glossed "sake meter value" in English, a remarkably content-free name. Unfortunately, it really is a pretty exact translation, as "nihonshu" (lit. Japanese alcohol) is how the Japanese refer to sake and "do" means "degree" (and yes, this is used for 25-degree temperatures, 90-degree angles and so on as well).

What it really is, however, is a measurement of the relative density of the sake, also known as specific gravity if you want to sound even more scientific. This would seem to be a pretty strange thing to worry about, but it turns out that density is directly correlated to the amount of residual unfermented sugar in the sake. As nihonshudo is a relative scale based on water at 0, positive numbers -- low density -- mean dry (karakuchi) sake and negative numbers -- high density -- mean sweet (amakuchi) sake. Do note that these are only general guidelines, many other things like acidity affect the perceived dryness of the drink.

"Normal" sake (ie. sake produced with a normal fermentation process) will have a nihonshudo around +2. Ratings above +6 or so are considered dry and ratings above +10 are considered rather silly, although I've once sampled a fairly ludicrous +25. Negative values, on the other hand, are not often seen, with the notable exception of unfiltered nigorizake.

Nihonshudo is included on a standard Japanese sake label as the fifth row from the top.