Remember that orbits are elliptical not circular, so the distance between the Earth and moon is not always the same. Yes, the Earth cases a shadow (which has two parts, a partial shadow that blocks some light and an inner shadow that block all light from the sun), but that inner shadow seldom covers the moon. When the inner shadow covers the moon, there is a lunar eclipse. Something else to understand, there is a point in space where the inner shadow disappears; at that point one can see a ring of the sun around the Earth (closer in, the Earth completely blocks the sun, further out more of the sun is visible). The point where the inner shadow disappears is usually inside the orbit of the moon, so the moon gets light.

Some full moons are dimmer then others because the moon is passing through the outer shadow.

The other factor that effects whether or not the moon gets light, is that the moon does not orbit the Earth in the same plane as the Earth orbits the sun. That means that most full moons happen when the moon is above or below the Earth in space relative to the Earth-Sun orbit plane (ecliptic).

Hope that helps.