It simply means not accessible to the general public, much as certain research areas in university libraries can only be accessed with special permission.
Those libraries have been open to researchers since the 1880’s. It’s just that you can’t have everyone and his brother pawing over a letter from Genghis Khan’s grandson, or it would disintegrate.
That's understandable. But it doesn't explain the "secret" in its title. I mean, the universities don't call their libraries "secret" just because they have restricted access.