When we see the fully illuminated side of the Moon, it looks "full" (like a big round circle). When the dark side of the Moon faces us, we can barely see it.
The lunar phase (the fraction of the Moon which is illuminated) depends on how much of the illuminated side of the Moon we can see (how much is visible from Earth).
When the Sun and Moon lie on opposite sides of the Earth (when we lie in between them), we see the entire illuminated side of the Moon.
When the Moon lies between the Sun and the Earth (near to the Sun in the sky), we can only (barely) see the dark, back side of the Moon.
Review this key concept in Example #1.