New Moon
The new moon is the lunar phase describing an absence of the moon. More correctly, the reflective portion of the moon is facing away from the Earth so that it appears on Earth that there is no moon. This occurs when the moon is in between the sun and Earth.
Waxing Crescent
A few days after the new moon phase, the moon's orbit moves it away from the direct path between earth and sun, and we begin to see a small crescent appear in our western sky. This small area is the visible portion of the moon reflecting sunlight. It appears small because we are seeing it at an acute angle.
First Quarter
About a week after the new moon phase, the moon is perpendicular with the Earth. The reflective portion of the moon that is visible to people on Earth covers the sunward half of the moon. It appears to be in the southern sky and move east through the night. It is sometimes referred to as "half moon" because the visible portion of the moon is half illuminated.
Waxing Gibbous
The waxing gibbous appears a few days later and appears to move further east. At this point, the reflective visible portion of the moon lies at an obtuse angle in relation to the Earth and we experience this as a moon that is more than halfway illuminated. The waxing gibbous only has a small portion of lunar surface that is not visible on Earth.
Full Moon
During a full moon, the moon appears on earth as a complete circular luminescent body. This occurs because the reflective portion of the moon is facing directly at the Earth. At this point, the moon is reflecting the most sunlight that it will reflect in its month-long cycle. Because the moon is constantly moving, true full moon lasts only a few moments, but we experience it on Earth as a few days in length.