During a new moon or "dark moon" phase, the moon is between the sun and the Earth. The side facing the Earth is completely dark because viewers on Earth are looking at the unlit or "night" side of the moon. When this moon phase is in perfect alignment with the sun and Earth, a solar eclipse occurs.
"Waxing" means increasing. During a waxing crescent phase, the moon appears to be one-quarter size and crescent-shaped, with the tips pointing to the left. During the middle of this phase, the moon is at a 45-degree angle to the sun and Earth.
The "half moon" or first quarter moon occurs when one half of the moon is illuminated and one half is not. It is still moving toward the full moon phase and looks like a capital "D" to the viewer. It is at a 90-degree angle to the Earth and sun.
"Gibbous" refers to the time when the moon is more than half visible. During this phase, the moon's visibility continues to increase as the moon revolves away from the sun. At the middle of this phase the moon is at a 135-degree angle from the sun.
The Earth is now roughly between the sun and the moon at a 180-degree angle. Viewers on Earth are able to see the entire moon's surface illuminated. When this moon passes through the shadow of the Earth a lunar eclipses occurs.
The moon begins to move back toward the sun side and appears to grow smaller or "wane." This phase shows only three-quarters of the moon with the light on the right side of the surface not visible. The midpoint of the phase is at a 135-degree angle from the sun.
The third quarter or "half moon" phase appears to be a backward capital "D." It is at a 90-degree angle to the sun and presents the viewer with a half-illuminated surface.
The middle of this phase is at a 45-degree angle to the sun and Earth and shows only one-quarter of the moon's surface. The tips of the crescent point to the right.