Caption: How the Earth's equatorial bulge and Earth's axial rotation leads to the axial precession.

Features:

1. The short explanation for the Earth's axial precession is gravitational perturbations.

2. Now for the long explanation.

3. The Earth is slightly oblate in that it has an equatorial bulge due to the centrifugal force caused by the Earth's rotation.

   The oblate isn't very large: the Earth equatorial radius R_eq_⊕ = 6378.1 km and the Earth polar radius R_po_⊕ = 6356.8 km: the difference is only 21.3 km (see Wikipedia: Earth).

4. The slightly different gravitational forces on the different parts of the equatorial bulge of the Earth (stronger on the near side to the source of external gravity, weaker on the far side to the source of external gravity) of the Moon, Sun, and, to a much lesser degree, the planets try to align approximately the bulges with the ecliptic plane, and thereby align approximately the Earth's axis with the ecliptic axis.

   The slightly different gravitational forces are the gravitational perturbations in this case.

5. The differential force of gravity is called the tidal force.

6. The tidal force in this case causes a torque in the physics terminology. A torque is a force-like quantity used to describe the "twisting" effect of a force.

   For example, people sometimes talk of torquing a screw.

7. If the Earth were NOT rotating, the Earth's axis would oscillate in the plane of the illustration if the outside gravitational force were in the plane of the illustration.

   The oscillation might be damped out in in time due to perturbations.

8. But the Earth is rotating on its axis.

   The Earth's rotation is the cause of the equatorial bulge via the centrifugal force.

9. With rotation, one gets axial precession, NOT oscillation.

10. There seems no simple way to understand why precession arises in this situation.

    The situation is somewhat similar to why orbiting objects don't fall inward under gravity.

    They keep falling, but keep missing because they have a sideways motion or, in physics terminology, angular momentum (which is a measure of rotation).

    Similarly, the axis of rotating Earth keeps trying to align perpendicular to the direction of gravity but keeps missing because the Earth has angular momentum about its axis

    The "missing" is the axial precession.

11. Rotational motion is actually just very tricky.

    But the odd effects of rotational motion are pretty commonly seen.

    For example, the upright orientation of bicycles is stabilized by the rotation of the wheels and precession is exhibited by toy tops and gyroscopes.