Most of the difference in the average lengths of the two kinds of year is due to the very slight change in the direction of the Earth’s rotation axis in space from one year to another. We usually think of the Earth’s axis as being fixed in direction – after all, it always seems to point toward Polaris, the North Star. But the direction is not quite constant: the axis does move, at a rate of a little more than a half-degree per century. So Polaris has not always been, and will not always be, the pole star. For example, when the pyramids were built, around 2500 BCE, the pole was near the star Thuban (Alpha Draconis). This gradual change in the direction of the Earth’s axis, called precession, is caused by gravitational torques exerted by the Moon and Sun on the spinning, slightly oblate Earth.
Because the direction of the Earth’s axis determines when the seasons will occur, precession will cause a particular season (for example, northern hemisphere winter) to occur at a slightly different place in the Earth’s orbit from year to year. At the same time, the orbit itself is subject to small changes, called perturbations. The Earth’s orbit is an ellipse, and there is a slow change in its orientation, which gradually shifts the point of perihelion in space. The two effects – the precession of the axis and the change in the orbit’s orientation – work together to shift the seasons with respect to perihelion. Thus, since we use a calendar year that is aligned to the occurrence of the seasons, the date of perihelion gradually regresses through the year. It takes 21,000 years to make a complete cycle of dates.
We would not expect the 21,000-year cycle to be very important climatologically because the Earth’s orbit is almost circular – the distance to the Sun at perihelion is only about 3% less than its distance at aphelion. That is, whether perihelion occurs in January or July, it seems unlikely that our seasons would be much affected. At least, that is the case now; but the eccentricity of the Earth’s orbit (how elliptical it is) also changes over very long periods of time, from almost zero (circular orbit) to about three times its current value. The eccentricity of the orbit varies periodically with a time scale of about 100,000 years. So, it would be reasonable to suppose that if the 21,000-year perihelion shift cycle were to have any effect on climate at all, it would only be during the more widely-spaced epochs when the orbital eccentricity was relatively large. That is, climatologically, the 100,000-year cycle of eccentricity should modulate the 21,000-year cycle of perihelion.
In fact, Mars has an orbit much more eccentric than the Earth’s, and its perihelion cycle (which has a period of 51,000 years) does apparently have a significant effect on climate and prevailing wind direction there.
This information comes from the US Naval Observatory: http://aa.usno.navy.mil/