The Moon goes through various phases: NEW MOON; CRESCENT/WAXING MOON; FIRST QUARTER; WAXING GIBBOUS; FULL MOON; WANING GIBBOUS; LAST QUARTER; WANING CRESCENT.
A fuller description of each follows.
The phases of the moon are caused by the positions of the Earth, Moon and Sun. The tides are affected by these positions too.
The Earth revolves around the sun taking a whole year to do so, and because the earth rotates we have day and night, each rotation takes 24 hours. The night sky shows when Earth faces away from the Sun.
The Moon produces no light of its own, it reflects the sunlight. Therefore at any one time there is a dark side and a light side on the Moon, as on Earth.
We see the Moon from earth and as the Moon orbits the earth, its position with the Sun changes, hence we get various phases of the Moon.
The Moon orbits the Earth anti-clockwise, which is the same direction as the earth’s spin and Earth’s orbit.
The NEW MOON occurs when the Moon is directly on the Sun side of the Earth; the Moon is ‘New’ when it is between Earth and the Sun. The NEW MOON rises and sets along with the Sun at about the same time, and has its shadowed face towards Earth.
After a few days the Moon has moved and a part of the Moon becomes illuminated by the sunlight producing a WAXING CRESCENT MOON soon after sunset. A WAXING CRESCENT MOON also occurs during the opposite part of its orbit, before sunset in the east. Careful observation on a clear night will reveal that the rest of the moon is very dimly lit; this is caused by sunlight reflecting off the Earth and shining on the Moon and reflecting back to Earth, this light is called Earthshine.
The Moon now moves into a right angle position with the Earth, a half-moon, but it is called commonly the FIRST QUARTER, there is another quarter illuminated on the far side of the Moon, and within a few days becomes WAXING GIBBOUS MOON. As the moon goes from new to full it is called ‘waxing;’ because it is gibbous, which is more than a quarter but less than full and waxing, which means it becomes more illuminated each night.
A FULL MOON is one that is fully illuminated by the Sun and follows the previous moon. Due to its positioning a FULL MOON rises in the east at about the same time as the sun sets in the west. A FULL MOON is very bright, some being brighter than others (Super moons) which make it very difficult to see detail in the night sky.
The FULL MOON now starts to wane, an old word that means diminish/decline, and after the FULL MOON the Moon now becomes a WANING GIBBOUS MOON, gibbous sine it is more than a quarter, but less than full, and waning as it declines.
This WANING GIBBIOUS MOON continues to wane as it continues its orbit and becomes a LAST QUARTER MOON, and again is at a right angle to the Earth-Sun line.
As the nights pass the Moon continues to wane and produces an OLD MOON, which is another (WANING) CRESCENT MOON, but it is the opposite side that is illuminated as a crescent.
The cycle is now completed and starts again back to the NEW MOON.
The above gives a brief description of the phases of the Moon. There are several in-depth and more comprehensive features to be found on the internet.