The Moon is covered with countless impact craters dug by all sorts of objects that hit it, from tiny dust particles to large asteroids. Both Earth and Moon move in the same region of the Solar System, so our planet should have gotten the same kind of bombardment. Possibly even more, because of the larger Earth gravity. Yet the surface of the Moon has many more impact craters. Why?
Our planet was indeed hit by many objects. But the surface of the Earth undergoes continuous change. Tectonic plates slowly drift, new mountains form, and volcanoes erupt. The atmosphere and water bodies slowly erode the surface. It takes a few tens of millions years to erase an impact crater, or significantly alter its appearance and make it unnoticeable. Over the past 4.5 billion years since the Earth-Moon system formation, however, the Moon kept a lot of its impact scars because it doesn't have enough energy to sustain such geological activity, and has no liquid water or significant atmosphere.