The Moon orbits around the Earth once every 27 days. An orbit is when something goes all the way around something else and returns to its starting position: the Earth orbits the Sun, and the Moon orbits the Earth. The Moon’s orbit is not circular - instead, it is an elliptical orbit. An ellipse is like an oval shape, or a stretched out circle. An ellipse can vary a lot in its shape: sometimes it is very long, stretched, and thin; other times it is nearly a circle.
The Moon’s elliptical orbit means that sometimes the Moon is closer to the Earth than at other times. At their closest, the Moon and the Earth are 360,000 km apart. When the Moon and Earth are close together, the point at which the Moon is at is called it’s “perigee”. When the Moon and Earth are far apart, the point at which the Moon is at is called it’s “apogee”. At the Moon’s apogee, the Moon and the Earth are 405,000 km apart. The line of apsides is an imaginary line between the Moon’s perigee and apogee.
Figure 1: The moon's orbit around Earth is in the shape of an ellipse. Image credit: NASA (public domain).
The discovery that the Moon’s orbit was in an ellipse shape was a very important scientific breakthrough. Scientists and mathematicians used to think that all celestial bodies orbited each other in circles. However, Johannes Kepler, a German mathematician and astronomer in the 17th century, spent a long time calculating how planets and the Sun moved in space, and theorised that the ellipse was the pathway that planets followed in their orbits. Kepler then tried to predict how Mercury would next move in front of the Sun (when viewed from Earth), based on his theory that the planets moved in elliptical paths rather than circular. His predictions about Mercury’s movement turned out to be correct, while everybody else’s were wrong.
Kepler’s work in astronomy earned him the respect and admiration of scientists in his own day, and in the modern world: NASA even named the Kepler space observatory named after him!
There is quite a big difference between how far away the Moon is at its perigee and apogee - so much so that the Moon can look quite different from Earth when it is at those two different points.
Figure 2: Lunar Perigee and Apogee. Image credit: Tomruen at en.wikipedia [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0)], from Wikimedia Commons
When the Moon is both a full moon, and at its perigee, this is called a supermoon. At this point, the moon looks 12% bigger, and 30% brighter than a regular full moon.
The Earth’s rotation is slowing down each year, due to friction caused by the Moon’s tidal pull on the Earth. As Earth’s rotation slows down, the gravitational pull of the Earth on the Moon weakens. So watch out - the Moon is slowly creeping away!
Time Magazine - Top 10 Things You Didn't Know About the Moon
Space.com - How Far is the Moon?