The precession of the equinoxes refers to the precession of Earth's axis of rotation with respect to inertial space.
The precession of the equinoxes is caused by the differential gravitational forces of the Sun and the Moon on the Earth.
In popular science books, precession is often explained by an analogy to a spinning top.
While the physical effect is the same, some crucial details differ.
In a spinning top, gravity causes the top to wobble which, in turn, causes precession.
The applied force is thus in the first instance parallel to the rotation axis.
But for the Earth the applied forces of the Sun and the Moon are in the first instance perpendicular to it.
Thus, the Sun and the Moon do not work on the rotation axis.
Instead they work on the equatorial bulge; due to its own rotation, the Earth is not a perfect sphere but an oblate spheroid, with an equatorial diameter about 43 kilometers larger than its polar diameter.
If the Earth were a perfect sphere, there would be no precession.