The beginning of the year 1393 in Iran will occur at 20:27:07 on 29 Esfand 1392. This article explains how that instant can be determined to an accuracy of less than one second.
For simplicity, first imagine the sky as a sphere upon which the stars, Sun, and planets are located. On this celestial sphere, just as on Earth, we imagine lines analogous to geographical longitude and latitude.
If Earth's North and South Poles are connected, the resulting line is the axis around which Earth rotates. Extending Earth's axis in both directions makes it intersect the celestial sphere at two points called the celestial poles. Thus, if you were standing at Earth's North Pole, the north celestial pole would be directly overhead and the south celestial pole beneath your feet.
We can also draw lines across the sky parallel to Earth's lines of latitude. These correspond to lines of declination. The circle formed where the plane of Earth's equator intersects the celestial sphere is called the celestial equator. It therefore lies directly above Earth's equator. For an observer on Earth's equator, the celestial equator appears as a semicircle joining east and west and passing directly overhead. At Earth's poles, it coincides with the horizon.
Every day we see the Sun rise in the east, travel across the sky, and disappear below the western horizon. We know that this daily apparent motion is caused by Earth's rotation. But the Sun has another apparent motion in the sky. If it were faint enough for the surrounding stars to remain visible, we could record its position among the stars each day and see it shift gradually against their apparently fixed background. This annual apparent motion results from Earth's orbit around the Sun. After roughly 365.24 days, the Sun returns to approximately the same position against the stellar background.
Plotting the Sun's position among the stars day after day traces its annual path across the sky: the ecliptic. In other words, the ecliptic is the projection of the plane of Earth's orbit onto the celestial sphere.
The ecliptic is not aligned with the celestial equator; the source gives their angle as 23°26′. They intersect at two points. Consequently, during its apparent annual journey the Sun lies sometimes north and sometimes south of the celestial equator. For observers in the Northern Hemisphere, this is why the Sun climbs higher in summer, its rays strike the ground more directly, and summer days are longer: the Sun then lies north of the celestial equator.
As the Sun moves from the southern half of the celestial sphere into the northern half, it crosses one of the two intersections of the ecliptic and celestial equator; moving back southward, it crosses the other. At these times the Sun shines directly over Earth's equator. The article calls these the equinox points and the corresponding instants the equinoxes. The spring equinox marks the beginning of spring and the autumn equinox the beginning of autumn. At the spring equinox, the Sun crosses from the southern celestial hemisphere into the northern one, after which daylight becomes longer than night for Northern Hemisphere observers.
Thus, the instant of the Persian solar New Year is, as its concept implies, the precise moment when the Sun passes through the spring equinox.
The article describes the development of this remarkable calendar as an achievement of Iranian scholarship and a valuable inherited legacy. Its designers were mathematicians and astronomers, the best known among them being the Iranian mathematician and poet Omar Khayyam. Working at the request of Seljuk ruler Malik-Shah and revising the Yazdegerdi calendar, these scholars developed the new solar calendar.
Note: Because a human lifetime is short compared with cosmic timescales, the Sun's annual path appears essentially fixed to us and passes through particular constellations. In ancient astronomy and astrology these regions were traditionally called zodiacal signs; for example, saying that the Sun was “in Virgo” meant that it appeared within that celestial constellation.