Bernard Foing wrote an article for Astrobiology Magazine about how our Earth, its weather, and its life forms would be different without the influence of the Moon.
The eyesight of many mammals is sensitive to moonlight. The level of adaptation of night vision would be very different without the Moon. Many of these species have evolved in such a way that their night vision could work in even partial lunar illumination, because that's when they are most active. But they can be more subjected to predators, too, so there is a balance between your ability to see and your ability not to be seen. The Moon has completely changed evolution in that aspect.
Human vision is so sensitive that we are almost able to work by the light of the Milky Way. The full Moon has more light than we need to see at night. For most of our history, we were hunting and fishing or doing agriculture, and we organized our lives by using the Moon. It determined the time for hunting, or the time where we could harvest. That's why most of our calendars are based on the Moon.