The moon may attract fewer bits of space rock than the Earth, but the moon is powerless to do anything about it after it has been hit. Once something hits the moon, that event becomes frozen in time. Earth, on the other hand, simply brushes these impact craters off and moves on with its life. read more
One main reason is that the Moon is fairly dead, metaphorically and literally, compared to Earth. Here on Earth, craters can disappear much easier, for a few reasons. read more
The moon has none of these factors to erode its craters (and little atmosphere to shield it). So the only things that have changed or eroded craters on the moon are volcanic activity (for older craters) and hits by even more meteors. Hence by the moon has so many more craters than we do. a few reasons. read more