Short answer: It controls whether the running game moves forward while you edit. In Live, your game plays normally - clicks advance, timers run, choices work. In Paused, forward progression freezes: clicks, Enter, timed pauses, choice selection, and video advance all hold, so you can work on a single frozen frame for as long as you like. Music keeps looping either way. The control lives in the top bar, and switching back to Live continues from wherever you parked.
Live - the game plays as you edit
Live is ordinary playback inside the editor. Click the stage and the story advances, timed pauses run out on their own, and choices take you down their branches - useful when you want to feel the pacing while you write.
Paused - freeze the frame
Paused holds every way the story moves forward: clicking the stage, pressing Enter, timed pauses, choice selection, and video advance. The frame stays put while you adjust it - reposition a sprite, rewrite the line, tune an effect - without the game slipping ahead mid-edit. Looping music keeps playing, so the scene still sounds like itself. One exception: payment prompts stay interactive even while Paused.
Clicking around while Paused
Click any event in the timeline and the playhead parks exactly on that step - any step at all, including ones with no visuals of their own, like setting a variable or a transition. The stage always shows exactly that moment, so you can inspect any point in the scene as a still frame.
Resuming
Switch back to Live and playback continues from the parked spot. A dialogue line still waits for a click before advancing, just as it would for a reader - resuming never lurches past the moment you were working on.
Where the control lives
It sits in the top bar as part of the playback control, next to the Reset button. On narrower windows the whole control collapses into a single dropdown that also carries Start over. Forge remembers which mode you left it in.