On the new moon, when the moon is between the earth and the sun, the light reflects back towards the sun, so you don't see it i.e. the moon is dark.
As for the full moon, the earth and sun are on the same side of the moon, so the sun is lighting the moon "from behind you" and you can see that.
I keep thinking there should always be a little bit of a solar eclipse when there's a new moon. I think my model might need a z axis. Or maybe something in my mental model just still isn't right.