The official name is the NRA National Match Gallery Course. It's shot in three stages, at 50 ft: slow fire, 10 shots in 10 minutes; timed fire, 2 strings of 5 shots in 20 seconds each; and rapid fire, 2 strings of 5 shots in 10 seconds each. The slow fire stage is shot on the NRA B2 target, the sustained fire stages are shot on the NRA B3 target.
The Gallery course is the typical so-called "bullseye" competition, shot with .22s, that a number of gun clubs participate in here in New England over the winter. It's typically shot indoors, although there is at least one rather infamous indoor/outdoor range where you shoot from indoors through window-like openings onto an outdoor range (dress warm for that one, especially in January).
As you indicated, a perfect score would be 300 - I've never actually seen one shot, but I've seen plenty of scores well into the 290s. The top competitors lose most of their points in slow fire, because the scoring rings on the B2 targets are much smaller than the same rings on the B3 target. In the leagues that I participate in, averages in the 260s are considered good, 270s very good, and 280s very good indeed. I don't personally know of anyone maintaining an average in the 290s, but they're out there for sure, although few and far between.
