The equinox happens when the equator passes the centre of the sun. This is when the north and south poles of the Earth are not tilted towards or away from the sun, as at other times, but are aligned so as to give, theoretically, the same amount of daylight in both of the Earth’s hemispheres.
After the autumnal equinox, the days get shorter and the nights get longer.
The equinoxes are the only times when the subsolar point (the place on Earth’s surface where the center of the Sun is exactly overhead) is on the Equator, and, consequently, the only times when the Sun is at zenith over the Equator. The subsolar point crosses the equator, moving northward at the March equinox and southward at the September equinox. The equinoxes are the only times when the solar terminator is perpendicular to the Equator. As a result, the northern and southern Hemispheres are equally illuminated. – wikipedia
Traditionally it signified when the farmers bought in the harvest, which perhaps explains why the full moon nearest the equinox is often called the harvest moon.
The oldest meaning of the word “equinox” is the day when daytime and night are of approximately equal duration. The word equinox comes from this definition, derived from the Latin aequinoctium, aequus (equal) and nocte (night).