Precession is the gradual change in the direction of the Earth's spin axis. The spin axis traces a cone, completing a full circuit in 26,000 years. If you've ever spun a top or a dreidel, the “wobbling” rotation of the top as it spins is precession.
Because the direction of the Earth's spin axis changes, so does the location of the Celestial Poles.
The reason for the Earth's precession is complicated. The Earth is not a perfect sphere, it is a bit flattened, meaning the Great Circle of the equator is longer than a “meridonal” great circle that passes through the poles. Also, the Moon and Sun lie outside the Earth's Equatorial plane. As a result, the gravitational pull of the Moon and Sun on the oblate Earth induces a slight torque in addition to a linear force. This torque on the spinning body of the Earth leads to the precessional motion.
Exercise:
Precession is easiest to see by osberving the Celestial Pole. To find the pole, first switch to Equatorial Coordinates in the View Options window, and then hold down the Up arrow key until the display stops scrolling. The declination displayed in the center of the Info Panel should be +90 degrees, and the bright star Polaris should be nearly at the center of the screen. Try slewing with the left and right arrow keys. Notice that the sky appears to rotate around the Pole.
We will now demonstrate Precession by changing the Date to a very remote year, and observing that the location of the Celestial Pole is no longer near Polaris. Open the Set Time window (Ctrl-s), and set the date to the year 8000 (currently, KStars cannot handle dates much more remote than this, but this date is sufficient for our purposes). Notice that the sky display is now centered at a point between the constellations Cygnus and Cepheus. Veryify that this is actually the pole by slewing left and right: the sky rotates about this point; in the year 8000, the North celestial pole will no longer be near Polaris!