It’s common knowledge that a day is 24 hours long. But if you measure the time from one solar noon to the next (when the Sun reaches its highest point in the sky), you’ll find that this interval is not exactly 24 hours: on most days it is slightly longer or slightly shorter.
This is not mainly due to seasonal changes in daylight length. Those changes mostly shift sunrise and sunset earlier or later in a way that is roughly balanced around midday, while the “noon” itself can drift relative to clock time.
This page explains why solar noon drifts through the year—a pattern described by the Equation of Time—and how the same effect produces the Sun’s analemma.
Understanding the difference between a sidereal day and a solar day is a prerequisite for this topic. If you want a refresher, watch this explainer: Sidereal vs solar day (YouTube).
Axial tilt is the main component shaping the analemma.
Look at the ecliptic path (the green circle on Earth), which traces the subsolar point through the zodiac markers.
Each day the Sun shifts slightly eastward along this circle across the year.
Suppose the subsolar point moves one degree per sidereal day on the ecliptic and follow how that translates to longitude.
At the equinoxes, a one-degree step corresponds to less than one degree of longitude, because the ecliptic is tilted relative to lines of latitude. The motion splits into eastward plus north/south components; the eastward part is less than one degree, so noon comes earlier than average.
At the solstices, the ecliptic is nearly parallel to lines of latitude and most motion is eastward. Because the Sun sits at a different latitude from the equator, longitude lines are closer together there, so one degree along the ecliptic becomes more than one degree of longitude; noon comes later.
The chart shows the early/late pattern over the year from tilt alone. This component alone would make a symmetric, regular figure-eight. The real analemma is wider in the southern lobe and asymmetric left/right, because of the other component: orbital speed.
In the tilt component we assumed the subsolar point moves one degree per sidereal day. In reality the daily step changes over the year.
The chart shows the pattern: the subsolar point moves more in January than in July because Earth's orbital speed varies. Earth is fastest near perihelion and slowest near aphelion.