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From Wikipedia:

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. The word comes from Latin Aequus, meaning “equal”, and Nox, meaning “night”.

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 start of the New Year in Hindu calendar and the Persian calendar or Iranian calendars as Nowruz (means new day), while the autumnal equinox (September) marks the beginning of autumn.