A "star gauge" is a special gauge intended to measure internal bore diameter. The idea of a star-gauged barrel was that, in an era when rifling processes could be a bit inconsistent (due to cutter wear in the "hook rifling" process causing high and low spots), the star-gauged barrel had been measured for consistent rifling the length of the bore. Therefore, the barrel would be "guaranteed" (or at least assumed to be) accurate.

In practice, "star gauging" appears to have been one of those half-skill-half-magic processes. Bill Brophy wrote, in his big book on '03s, that he and a friend each had a star gauge, and a NOS star-gauged barrel with the original measurement card. They tried each others' gauges on each others' barrels, and neither of them could come close to each others' gauge readings, let alone the "official" readings from the Armory.

As to accuracy, I've seen multiple statements that the plug-rifled and air-gauged barrels from WW2 are every bit as good, if not better. I can report that my Springfield target rifle has a 1944 High Standard barrel on it, and that sucker shoots better than me!