Does this mean that we've moved, or that it has moved?
In general,, the spacing between the Earth, Moon, and Sun has changed so that we on Earth are seeing a different portion of the illuminated side of the Moon.
Hold your two fists about 12 inches in front of you at eye level, with the right fist directly in front of you and the left arm half extended leftwards . The left fist represents the Sun, the right fist represents the Moon, and your head is the Earth. As the sun shines on the Moon, illuminating the half of it that faces the Sun, the Earth sees a vertical half-Moon (more or less). That is, the left side of your right fist is illuminated, the right side of it is dark, and your eyes see half of the illuminated portion and half of the dark portion.
Now move your right fist upwards. As your right fist moves upward, the illuminated portion of it that is visible from your head moves downwards on the surface of it.
Moving both fists upwards (or the head downwards) does not produce the same effect, exactly.
So, I deduce that the Moon has moved.