To picture the effect of the Moon’s gravity on the planet Earth, draw two lines starting at the very center of the Moon which gradually spread away from each other until they just graze the Earth at its opposite edges. That makes a long, narrow “vee” with the Moon at its point and the Earth held between its open ends.
Earth is pulled into, or falls into the vee due to gravitational attraction, so its sides get squeezed in the narrowing slot. This results in the Earth bulging slightly toward the Moon, and on the opposite side, away from it. Imagine gently squeezing a balloon between your hands held in a vee-shape. The sides will flatten and the front and back will bulge.
The same thing happens to the Earth’s ocean, with the bulges being experienced as tides on opposite sides of the planet. There is a similar effect in the atmosphere, though it’s not as noticeable as the ocean tides. As Earth rotates, the tides remain fixed, pointing at and away from the Moon.
The bulges aren’t exactly the same. Because it’s a vee-shaped squeeze, the bulge facing the Moon is slightly pointier and the one facing away is slightly broader. This has been observed in ocean tides, which are slightly higher on the Moon side.
It makes for quite a picture to imagine our planet being kneaded by gravity, but that’s not all of it. It seems that the continuous westward movement of the bulges is resulting in a tiny movement of the Earth’s crust itself. Floating on the sticky, molten magma below it, the crust is free to be pulled ever so slightly back against the rotation of the planet, resulting in a very slow general drift westward. The rate might be in the centimeters per century range.
In addition to larger effects like spreading sea floors and upwelling magma plumes, it looks as if gravitational drag is contributing a small but steady force in the constant evolution of the surface of our planet.