When you travel by train and look out the window, you'll feel the lamp posts and houses all run backwards. But when you look carefully, you'll find the objects closer to the train run faster than those farther away. Mountains and big trees seem to follow you.
The moon, hanging high in the sky, is very, very far from us. No matter where you go, you can always see the moon. That's why we feel that the moon always follows us wherever we go.