Basically, it's used to describe what the bore looks like when you look down it. If it's been shot with corrosive ammo and hasn't been maintained or cleaned properly, the bore will look dark due to the corrosion, rust, pitting etc. Light won't really shine well off the metal if that's the case. Sometimes a dark bore can just be from the fact that it hasn't been cleaned well in years/decades, so there's a lot of crud built up in the grooves. Obviously, if a bore is described as shiny that usually means light reflects off it well. This is usually it's a sign that the bore has been cleaned and maintained pretty well. I imagine most, if not all, collectors prefer a bright bore, though that's not the only criteria when looking at milsurps.
To me it doesn't really matter if a bore is 'dark' as long as the rifling is still crisp and sharp. The crud can usually be cleaned out, especially after running some rounds down it. I've had a number of milsurps that cleaned up quite well with a good cleaning and a couple of range sessions. The problem with the 2 terms is that they are very subjective...there's a large difference between a dark bore that looks like a sewer pipe with little rifling left, and a dark bore that just has decades of carbon build up in it.