There's both practical and more spiritual/philosophical reasons for this.

Before artificial light sources, especially electrical ones, moon light let people stay productive longer whilst outside. This was especially important for comunal activities like hunting, harvests or celebrations too. Keeping track of moon cycles is thus valuable for preparation in scheduling. And once you do that it can also be used to organize other social events around that. Similar to how our modern calendars and schedules are built around important fixed events.

The moon and sun as celestial bodies also gained prominent religious and mystical significance in ancient cultures. Remember that people didn't actually know what the moon or sun were in the modern scientific sense. But for some strange reason these mystical glowing disks on which people were so reliant kept rising with unerring synchronicity. The inquiry into the movements on the firmament lead many a civilization down the paths of observation, record keeping and math too.