[dredmorbius]

"What was the significance of cycles of the moon in the past?"

Really not my metier, but a few thoughts.

The Moon is highly significant if you're living along a coastline (and most humans do) as the tides are directly related.

In a pretechnological society, the biggest and cheapest source of night-time lighting was moonlight (though you could locally out-shine it with torches, candles, or lanterns). For travel or any sort of nocturnal activity (including ocean navigation), you'd likely take it into consideration.

In arctic cultures, moonlight might be your only light for much of the year, and on snow, full moonlight is amazingly brilliant.

In terms of dividing up the the year, different moons, particularly named moons ("hunters", "harvest", etc.) are significant.