There are two different meanings for the phrase “the dark side of the moon,” when one is discussing astronomy rather than Pink Floyd. In the technical sense, astronomers use it to refer to the side of the moon which is not illuminated by the sun. The location of the dark side of the moon changes depending on where the moon is in its orbit. Some people mistakenly mention refer to the the far side of the moon as the dark side, the side of the moon which we never see from Earth due to a trick of the relationship between the moon and the Earth.
Several factors come together to cause the far side of the moon to face away from Earth, including the orbits of both bodies. As the moon orbits the Earth, tidal forces interact between the two to force one side of the moon to always face the Earth. The features of this side of the moon are familiar to many people on Earth, with many maps and photographs available for people who want to learn more about the details of the near side of the moon. Many people are surprised to learn that the far side of the moon is radically different from the near side, as was proved when spacecraft took photographs of it.
The far side of the moon is deeply pitted due to collisions with asteroids and meteors. Some of these pits are quite large; the South Pole-Aitken Basin, for example, is famously huge. It is believed to be the largest impact crater in the solar system. The deepest pits and craters on the moon's surface are known as maria, after the Latin word for “seas,” since early astronomers thought that the moon was covered in oceans. Since the far side of the moon never faces the Earth, some astronomers have discussed installing a radio telescope on it with the intent of studying the universe without interference from transmissions on Earth.
As the moon orbits the Earth, different parts of it are illuminated by sunlight. When the moon is between the Earth and the sun, it appears entirely dark, and as it moves, more of its surface reflects light, causing the moon to appear to grow in size until it becomes full, entirely illuminated by the sun. When the moon is full, the dark side of the moon is also the far side of the moon, but otherwise the two terms are not interchangeable. As the moon moves out of full, it wanes or dwindles in size until it becomes dark again, and the far side of the moon is the side which is totally illuminated, although we cannot see it.
The confusion between the dark side of the moon and the far side of the moon is common. Many people use the term poetically to describe extreme isolation, in which case “dark” tends to scan better than “far.” Astronomers greatly appreciate it when people use the terms correctly, since they do in fact refer to different things.