Procession is the movement of the rotational axis of an object. It is commonly seen in toy tops, but all spinning objects can demonstrate procession. In astronomy, we are most interested in the procession of Earth. The orbital tilt obliquity of Earth is 23.5 degrees.
Thus, the axis of Earth's rotation traces out a cone of half-angle 23.5 degrees in a period of roughly 26,000 years. This effect is often referred to as precession of the equinoxes. The technical details behind precession are beyond the physics covered in introductory astronomy, but they focus on the fact that Earth is not spherically symmetric, but oblate, fatter around the middle. and the gravitational pulls of the Sun and Moon on this equatorial bulge cause precession. I will demonstrate precession with what is known as an air gyroscope.
This particular model was manufactured by Ealing Corporation in 1956. We will observe precession on this 4-inch steel ball, and a pump will force air out a hole beneath the ball, supporting its weight and minimizing friction. Note that the ball has a rod attached, so one can view the ball spinning. Part of the interior of the ball has been hollowed out to counterbalance the weight of the rod. I will turn on the air pressure and position a weight at a predetermined balanced position.
Thus the center of mass of the ball rod weight is over the center of the ball. When we spin up the ball we see that it will spin stably for a long while in this balanced position. I now move the weight outward.
The ball is no longer balanced and it is more analogous to the oblate Earth. When I spin up the ball, we can now readily observe the slow change of the axis of rotation due to precession. Now remember that Earth's axis of rotation forms the basis for the celestial equatorial coordinate system.
Thus, as the location of the vernal equinox and celestial poles change due to precession, the positions of stars in right ascension and declination also change. So although right now we have a fairly bright star in Polaris near the north celestial pole, that will no longer be true in about a thousand years. Astronomical catalogs giving the positions of objects are typically updated every 50 or 100 years to the definition of the celestial equatorial system at that time, such as 1950 or 2000. And computer programs to process object coordinates to that system at the current time are ubiquitous. A telescope pointing system that doesn't take precession into account wouldn't be sufficiently accurate to be very useful. More teaching materials can be found on the web at astro.unl.edu.