What does this motion tell us about the Earth's motion in space? If you ever had a spinning top, you know that its axis tends to stay lined up in the same direction --- usually, vertically (left figure), though in space any direction qualifies.
Give it a nudge, however, and the axis will start to gyrate wildly around the vertical, its motion tracing a cone (right figure). The spinning Earth moves like that, too, though the time scale is much slower --- each spin lasts a day, and each gyration around the cone takes 26 000 years. The axis of the cone is perpendicular to the plane of the ecliptic.
The cause of the precession is the equatorial bulge of the Earth, caused by the centrifugal force of the Earth's rotation (the centrifugal force is discussed in a later section). That rotation changes the Earth from a perfect sphere to a slightly flattened one, thicker across the equator. The attraction of the Moon and Sun on the bulge is then the “nudge" which makes the Earth precess.
Through each 26,000-year cycle, the direction in the sky to which the axis points goes around a big circle, the radius of which covers an angle of about 23.50 degrees. The pole star to which the axis points now (within about one degree) used to be distant from the pole, and will be so again in a few thousand years (for your information, the closest approach is in 2017). Indeed, the “pole star" used by ancient Greek sailors was a different one, not nearly as close to the pole.
Because of the discovery made by Hipparchus, the word “precession" itself no longer means “shift forward" but is now applied to any motion of a spin axis around a cone--for instance, the precession of a gyroscope in an airplane's instrument, or the precession of a spinning satellite in space.
Precession of a spinning scientific payload (also known as its “coning" --- from “cone" --- or its “nutation") is an unwelcome feature, because it complicates the tracking of its instruments. To eliminate it, such satellites use “nutation dampers," small tubes partially filled with mercury. If the satellite spins as it was designed to do, the mercury merely flows to the part of the tube most distant from the spin axis, and stays there. However, if the axis of rotation precesses, the mercury sloshes back and forth in the tube. Its friction then consumes energy, and since the source of the sloshing is the precession of the spin axis, that precession (very gradually) loses energy and dies down.
In the section on the calendar, we saw that the Earth's rotation is slowed down very gradually by the tides, raised by the gravity of the Moon. That process is a bit similar to the action of nutation dampers: the energy of the tides is “lost"--that is, converted to heat--when the waves caused by tides break up on the seashore, and that loss is ultimately taken away from the rotational motion (not the precession) of the Earth.