This prcession will affect the motion of the Sun within the year and consequently the length of the seasons since the Earth moves faster in its orbit near perihelion and slower near aphelion. The lengths of summer and winter are an important factor in long term climate change.
*Edit: The subscript "a" refers to the anomalistic year which is the time between one perihelion and the next. It is slightly different than the time between successive Vernal Equinoxes.
Supplemental: With apsidal precession one could "fix" the date of the Vernal Equinox but the Autumnal Equinox and the solstices would vary slightly relative to it over time due to changes in the length of the seasons. All the dates would still vary over a four year period because of the leap day.