Board Game Arena

There is a crescent moon next to the tournament clock that appears to influence when the clock does or does not countdown during a players turn.
Can someone explain how this works please?

I don't know for tournaments. But for normal games, when the speed is set to fast turn-based (more than 4 moves per day), there's only a 12-hour period where the clock moves (the table creator decides which exact period). You can still play outside this period, but your clock doesn't move. And this is for all games, not just Backgammon.

Okay, thank you, that makes sense. Is there any way to check what are the active hours?

In the game, check the "Options" tab at the bottom.