(thanks to Wade Clark at Skychasers)
Go outside and look at the moon at night. How much of the moon can you see? If you go someplace really dark, like out in the country camping, and look carefully, can you see the rest of the moon that is in shadow? That's the shadow of the Earth blocking the sunlight from the moon. You can see it because some sunlight reflects off the Earth and reaches the moon that way (You can see it in this picture).
See how the shadow of the Earth is curved? That's because the Earth is round, so it makes a curved shadow like a ball. Try this experiment: put a small ball on the ground outside in the sunlight. Now the sun shines on it and lights it up like the sun also lights up the moon. Now hold a bigger ball between the sun and the small ball. Try to line it up so that the shadow of the big ball falls on the small ball. What happens? Try it again using different shape things instead of the big ball: a piece of paper? A shoebox? What kind of shadow do you see?