Fixed stars are all those objects in the sky that do not appear to move in relation to each other, but still seem to collectively move across the sky. The term "fixed" was used in ancient times to set them apart from "wandering stars," which were those bodies in the sky that did change position. In other words, the sun, moon, and planets in our solar system were referred to as "wandering stars" because they change position in the night sky. Fixed stars, on the other hand, appear to remain in relative position to each other, allowing them to be seen as constellations and similar groups.
The idea of fixed stars and those that wander is not scientifically accurate, but the term is still used to refer to concepts held in the past. Ancient cosmological models typically held that the Earth was located at the center of the universe and that all other observable bodies moved around it in some way. Beyond the Earth, it was believed, were a number of celestial spheres on which the various stars were affixed, allowing them to move around the Earth while remaining relatively stationary with respect to each other. Fixed stars were those bodies that were upon such a sphere and moving together around the Earth.
All of the objects now referred to as "stars" were fixed stars, since they do not seem to move in relation to each other. These distant stars do, in fact, move and are constantly moving away from each other and in relation to each other. Most of the objects visible from the earth are within the Milky Way galaxy, which is the collection of stars and other bodies of which the earth is a part. In addition to the motion of fixed stars away from each other, they are also spinning slowly around the center of the Milky Way and may be in orbit around other bodies.
Those objects in space other than the fixed stars were called wandering stars in the ancient model of the universe. They were basically the sun, which is the star closest to the Earth around which the earth revolves, the moon, and the other planets in the Earth's solar system. All of these objects seemed to change position relative to each other and other stars, because they are much closer to the Earth and their movements are more perceivable. The movements of many fixed stars are so slight and subtle that there are constellations that remain very similar to how they appeared from Earth thousands of years ago.