New Moon
According to NASA, a new moon occurs once every month when the moon is lined up between the sun and the Earth. During a new moon, the moon is at its closest to the sun. At this time the night sky appears dark and moonless. No moon is seen because the light from the sun is blocked and the part of the moon that faces the Earth is dark.
Crescent
A crescent moon appears twice a month, just before and after the new moon. A crescent is as it sounds; only a sliver of the moon is visible. This occurs when the moon is blocking most of the light coming from the sun and only a small portion of it is reflecting toward the Earth. Prior to a new moon, the crescent is waning. Waning refers to when the moon appears to be shrinking in the sky as it approaches a new moon. As the moon passes between the Earth and the sun, a new moon occurs. Just after the new moon is a waxing crescent. The term waxing is used when the moon is appearing to grow larger in the sky approaching a full moon.
Quarter
A quarter occurs twice a month and refers to when exactly one quarter of the moon is visible. This appears as a half moon in the night sky. When the moon, the Earth and the sun form a 90-degree angle with the Earth at the corner a quarter moon appears. A first quarter moon appears after a waxing crescent as the phases approach a waxing gibbous. A third quarter moon appears after a waning gibbous as the phases approach a new moon.
Gibbous
A gibbous occurs twice a month when the moon is either approaching or receding from a full moon. During a gibbous phase, more than half the moon is visible but it's not quite full. During a waxing gibbous, the moon is approaching a full position and the Earth is not quite lined up between the moon and the sun. During a waning gibbous, the moon is approaching third quarter and appears to be getting smaller.
Full Moon
A full moon is the moon's half way point during its cyclical journey and the farthest point the moon gets from the sun. This occurs when the Earth is between the moon and the sun. The moon is usually not on the same elliptical plane that the Earth and sun are on. Because of this fact, the sunlight reaches a full moon without being blocked by the Earth's shadow and a full moon appears. When the moon does pass across the elliptical plane, the shadow of the Earth blocks the sun and a lunar eclipse occurs.