What is meant by a lunation?

A lunation is the cycle of phases in one synodic month, starting and ending with a "new moon". This is slightly longer than the sidereal lunar month, in which the Moon revolves once around the Earth, because of the additional effect of the Earth's revolution around the Sun.

The new moon occurs when the Moon is between the Earth and the Sun, and the face towards the Earth is entirely in darkness. Over the next week (roughly), it waxes through the familiar crescent phase until the "first quarter", when the direction of the Moon from the Earth is perpendicular to that of the Sun, and the eastern half of the Moon's disc is illuminated.

During the second week it is "gibbous" - the majority of the nearside is illuminated and only a diminishing crescent remains in darkness, culminating in the "full moon" when the Moon and the Sun are on opposite sides of the Earth.

Over the next two weeks the Moon wanes again, through gibbous to "last quarter" - when the western half-disc is in light - and on through crescent to another new moon.