The most significant effects on Earth by gravity are its generally spherical shape and the relatively small disruptions in this shape.
The primary cause for the Earth's spherical shape is that it has enough mass, and therefore enough gravity, to rearrange itself into that shape. A sphere evenly distributes the gravity generated by the Earth's mass in as equitable a way as possible, whereas we could visualize a square planet experiencing uneven stress at its vertices.
The Earth isn't a perfect sphere for a variety of reasons. One is the fact that it's rotating, which causes a bulge along the equator, similar to the forces one would feel while on a merry-go-round. The Earth also has a moving bulge caused by the the force of the Moon's gravity pulling the Earth toward it.
Finally, there are smaller gravitational disturbances caused by differences in the density of rock throughout the crust. Mountain ranges tend to have higher-than-average gravity because they are underlain with very dense rock for several miles, whereas oceans are relatively lighter because water is far less dense than rock.
While this is the standard explanation for how gravity affects Earth's shape, the latest scientific research and reasoning gives a more complex explanation. The end result of this new perspective is that the direction of gravity and the surface of gravitational potential effect the shape of Earth by producing a geoid that is irregular in shape producing an irregular rotation.