It’s referring to how the scenes play out throughout the series. For example in the Starlight Revue movie, the cast would be fighting on a moving train but then the wind stops and random floating spotlights appear next to them, which allude to their performance starting. I love that kind of mix between reality and immersion : P
Same, to this day I don’t think I’ve enjoy a stage play series as much as Act-Age. Oshi no Ko’s stage play arc came close (what’s currently covered in the anime S2). It’s a shame because I know Act-Age would be an awesome anime when it’s adapted, too bad : (