Axial precession is the generalisation of the phenomenon of the precession of the equinoxes. When you spin a gyroscope on a table, the axis of the gyroscope will slowly rotate in the direction opposite of the spin. Roughly the same thing happens with the Earth (except there's no table).
This means that the directions of North and South are not constant, as measured on the celestial sphere relative to distant stars. They slowly trace a circle, with 'radius' of about 23.5 degrees, about once every 26,000 years. However, North and South as measured on the ground is constant - a road leading North, for example, will lead North always, but will point to a different star at different times in the 26,000 year cycle.
There is another effect, which is perpendicular to the effect of the axial precession. The radius of the circle described by the pole on the celestial sphere is not constant, it varies by a few degrees, with a period of about 41,000 years - so the resulting curve is rather like a pattern drawn by a spirograph toy.
Not to be confused with the precession of perihelion, which is a wholly different effect. The Earth's orbit is slightly elliptical, which means that sometimes it's closer to the sun than other times. The point at which the Earth is closest, called perihelion, does not occur at exactly the same time every year. This effect has a period of about 21,000 years.