Out of what we know about the moon so far – that it is the Earth's only natural satellite and only one side is visible to our planet because of its synchronous rotation – other influences the moon exerts on the Earth remain obscure except for its gravitational force.

The gravitational pull of the moon causes the rise and fall of the tides on the Earth. To be precise, the tides are the result of both the moon's and the sun's gravity. Since the moon is much closer to us than the sun, its gravitational gradient plays a much stronger role than the sun does to the Earth. When the sun and the moon are aligned, the gravitational pull becomes the strongest, leading to extra strong tides.

One of the most famous tidal bores can be seen in Qiantang River in eastern China's Zhejiang Province. During the tide, huge waves race against the current, form tides several feet tall, and continuously batter the bank. This phenomenon is partly due to the shape of the river as its estuary is shaped like a funnel, but the moon's gravity plays an important role.

Aside from its physically observable influence on the Earth, the moon holds mystical significance and is often deemed the culprit of abnormal behavior in humans and other animals. 

Take the full moon effect. Stories of people going crazy and howling like a wolf during a full moon can even be traced back to the Middle Ages. Anecdotes that the full moon causes epilepsy and strange behavior in pets seem to imply that a connection exists. However, after years of observation and study, no evidence has been found linking the moon to these abnormalities.

One likely explanation for these associations is that when strange things happen on a full moon, people tend to notice it and make a connection. But when strange things happen at other times, they don't make a connection to anything noticeable.