The earth has an atmosphere. When the earth passes through a cluster of asteroids (this is what causes meteor showers) the vast majority of them burn up in the atmosphere due to air resistance before they can reach the ground to make a crater. The moon technically also has an atmosphere but it is so thin that we don't really consider it an atmosphere. It can't be breathed and it won't slow down, heat up, and burn away objects that pass through it like earth's atmosphere. This means that when the earth and moon pass through an asteroid field the earth is protected while the moon just gets slammed over and over again.

On top of that, the earth has geological activity such as erosion which can erase the signs of old meteor impacts. The moon doesn't have this so every time a meteor strikes, the crater remains there until another meteor hits and obscures or covers it up with another crater.