The most notable affect of the moon is its creation of tides here on Earth.
Tidal forces occur from the gravity differential across an object. The force of gravity [from the moon] on the Earth is different depending on which side of the Earth you are on.
This tidal force
pulls on the Earths oceans. Most of the water is pulled
towards the moon, while the gravitational differential creates
an equipotential bulge on the opposing side of the body.(https://www.lhup.edu/%7Edsimanek/scenario/Field_tidal.jpg)