How Phases Occur
Picture the Sun shining toward the Earth-Moon pair on one side. Now picture the Earth, with the Moon at a place in its orbit around Earth that puts it between the Earth and the Sun. That means the Sun is shining on the side of the Moon that is facing the Sun. The side facing the Earth is dark in what is known as a New Moon. Say the opposite is true: the three bodies are ordered Moon, Earth and Sun. In this case, a person looking at the Moon would see it fully illuminated--the Full Moon. At the points in between the Full Moon and New Moon, varying degrees of light will illuminate the Moon from Earth's perspective, giving us the phases.
Phase Cycle
The lunar phase cycle goes from New Moon to New Moon and takes 29.5 days to complete. There are eight phases in each cycle that are recognizable by how much of the Moon is illuminated and the shape the visible part creates. The "age" of the Moon is the time that has passed as the cycle progresses, counted from the last New Moon. Besides the Full and New Moons, the other phases are the waxing and waning crescent, the First and Last Quarter, and the waxing and waning gibbous.
New and Full Moons
The New Moon, as the beginning of the lunar cycle, marks a "newly born" Moon. The "age" of the Moon is the time in days that has passed as the cycle progresses, counted from the last New Moon. After the New Moon, the Moon is said to be waxing--that is, growing larger. The Full Moon is the halfway point of the phase and after it appears, the Moon is said to be waning, disappearing as the Moon cycles toward another New Moon.
Crescent Moons
The crescent Moons, as the name suggests, look like crescents. The waxing crescent Moon appears after the New Moon, while the waning crescent Moon appears as the last phase before another New Moon appears. Crescent Moons are less than half-lit by the Sun as seen from Earth. The crescent phases each last about a week. Months in the Islamic Calendar begin with the first appearance of the waxing crescent Moon.
Quarter Moons
The Quarter Moons are split vertically by the light, with one half illuminated. The reason this Moon is called a Quarter rather than a Half Moon despite its illumination is because, counting the other side of the Moon, only a quarter of the Moon is lit as seen from Earth. The First Quarter Moon appears after the Waxing Crescent. The Last Quarter Moon comes before the Waning Crescent. The First Quarter Moon is left-sided; the Last Quarter Moon is right-sided. Along with the Full and New Moons, the Quarter Moons are considered primary phases.
Gibbous Moons
The waxing gibbous Moon and the waning gibbous Moon appear before and after the Full Moon, respectively. They are more than half-full--in other words, there is a crescent of the disk that is darkened. The gibbous phases each last about a week. These phases along with the crescent phases are considered intermediate phases.