What is procession of the equinoxes, and how does it relate to religion?

The Earth's axis of rotation precesses. which means that it rotates and wobbles.

To put it in perspective, consider the Vernal Equinox. This is the moment in time when the Sun crosses the equator in a northerly direction. More important is the direction of the Vernal Equinox, which is the line taken from the centre of the Earth to the Sun at the moment of the equinox.

If you take the direction of the Vernal Equinox for a particular year, the next Vernal Equinox will occur before the Earth reaches the same position with respect to the fixed stars. The tropical year, which is the time between Vernal Equinoxes, is shorter than the sidereal year, which is the time taken to complete a complete orbit with respect to the fixed stars, by about 20 minutes. This is due to precession.

The most notable relation of this to religion involved the Catholic Church. Easter Sunday is the first Sunday after the first full moon after the Vernal Equinox. The Catholic Church calculates the date of Easter based on the Equinox being 21 March. In 1582 the precession had caused the Vernal Equinox to slip back to 10 March. Pope Gregory XIII had to correct this by introducing the Gregorian Calendar and deleting 10 days from October 1582.