Glossy bounces in Cycles: bounces counting
With glossy bounces set to 1, the mirror in the background mirrors from the mirror in the foreground only that part, where the foreground mirror reflects the light (environment texture) of the world background, since there'e 2 glossy bounces (bounces counting in Cycles starts with 0 !):
I'm talking about the camera rays hitting the background mirror first (glossy bounce number 0) and then the outer areas of the foreground mirror (glossy bounce number 1) before hitting the world background. The black square in the background mirror is caused by the rays coming from the foreground mirror and hitting the background mirror which would cause a third glossy bounce (number 2) that isn't allowed with the current glossy bounces counter set to the maximum glossy bounce number 1.