i would draw a picture for you if could.
the suns rays do not land on half of the earths surface at any given time.
when its night, the sun isnt shedding light on your half of the planet.
the suns rays are filling up that dark night sky above you, and if anything was up in that space it would shine bright as if it was day time. but since that space is empty, there is nothing to reflect the suns rays back down to your eye balls, and all stays dark.
the moon is up there in the sky, recieving a face full of sun rays, reflecting some of them down into your eye ball whenever you look in its direction. which is why its lit up.