An equinox is an astronomical event in which the plane of Earth’s equator passes through the center of the Sun, 
which occurs twice each year, around 20 March and 23 September.
On an equinox, day and night are of approximately equal duration all over the planet. They are not exactly equal, however, due to the angular size of the sun and atmospheric refraction. To avoid this ambiguity, the word equilux is sometimes used to mean a day in which the durations of light and darkness are equal. [note 1] See Length of equinoctial day and night for further discussion.
The oldest meaning of the word “equinox” refers to a day when daytime and nighttime are of approximately equal duration. 
The word “equinox” comes from this definition and is derived from the Latin aequinoctium, aequus (equal) and nox (genitive noctis) (night).
Equinoxes on Earth
The equinoxes are the only times when the solar terminator (the “edge” between night and day) is perpendicular to the equator. As a result, the northern and southern hemispheres are equally illuminated.
In other words, the equinoxes are the only times when the subsolar point is on the equator, meaning that the Sun is exactly overhead at a point on the equatorial line. The subsolar point crosses the equator moving northward at the March equinox and southward at the September equinox.
The equinoxes, along with solstices, are directly related to the seasons of the year. In the northern hemisphere, the vernal equinox (March) conventionally marks the beginning of spring in most cultures  and is considered the New Year in the Persian calendar or Iranian calendars as Nouroz (means new day), while the autumnal equinox (September) marks the beginning of autumn. In the southern hemisphere, the vernal equinox occurs in September and the autumnal equinox in March.
Illumination of Earth by the Sun at the March equinox
The Earth in its orbit around the Sun causes the Sun to appear on the celestial sphere moving over the ecliptic (red), which is tilted on the equator (white)
Diagram of the Earth’s seasons as seen from the north. Far right: December solstice.
Diagram of the Earth’s seasons as seen from the south. Far left: June solstice.
When Julius Caesar established the Julian calendar in 45 BC, he set 25 March as the date of the spring equinox. Because the Julian year (365.25 days) is slightly longer than the tropical year, the calendar “drifted” with respect to the two equinoxes — such that in 300 AD the spring equinox occurred about 21 March. By 1500 AD, it had drifted backwards to 11 March.
This drift induced Pope Gregory XIII to create a modern Gregorian calendar. The Pope wanted to continue to conform with the edicts concerning the date of Easter of the Council of Nicaea of AD 325, which means he wanted to move the vernal equinox to 21 March, which is the day allocated to it in the Easter table of the Julian calendar. However, the leap year intervals in his calendar were not smooth (400 is not an exact multiple of 97). This causes the equinox to oscillate by about 53 hours around its mean position. This in turn raised the possibility that it could fall on 22 March, and thus Easter Day might theoretically commence before the equinox. The astronomers chose the appropriate number of days to omit so that the equinox would swing from 19 to 21 March but never fall on the 22nd (although it can in a handful of years fall early in the morning of that day in the Far East).
Spring equinox and fall (or autumn) equinox: colloquial names based on the seasons. However, these can be ambiguous since the northern hemisphere’s spring is the southern hemisphere’s autumn, and vice versa. The Latinate names vernal equinox (spring) and autumnal equinox (fall) are often used to the same effect.
March equinox and September equinox: names referring to the months of the year they occur, with no ambiguity as to which hemisphere is the context. They are still not universal, however, as not all cultures use a solar-based calendar where the equinoxes occur every year in the same month (as they do not in the Islamic calendar and Hebrew calendar, for example).
Northward equinox and southward equinox: names referring to the apparent direction of motion of the Sun. The northward equinox occurs in March when the sun crosses the equator from south to north, and the southward equinox occurs in September when the sun crosses the equator from north to south. These terms can be used unambiguously for other planets.
First Point of Aries and first point of Libra: names referring to the astrological signs the sun is entering. Due to the precession of the equinoxes, however, the constellations where the equinoxes are currently located are Pisces and Virgo, respectively.