Equinox
An equinox is one of the two days each year, around March 20 and September 22, when the Sun is directly over the equator and day and night are nearly equal.
Definition
An equinox is one of the two days each year, around March 20 and September 22, when neither hemisphere leans toward the Sun and daytime and nighttime both last close to $12$ hours everywhere on Earth. The Sun then stands directly over the equator, its rays striking Earth's axis at a right angle, so the terminator passes through both poles; the March equinox opens spring in the Northern Hemisphere and autumn in the Southern, and the September equinox reverses that. Precisely, the equinoxes are the instants when the Sun crosses the celestial equator, at ecliptic longitudes $0^\circ$ and $180^\circ$, so its declination is exactly zero, and the March point also anchors the origin of right ascension and the tropical year. Precession carries that point westward about $50$ arcseconds a year, a full circuit taking roughly $25{,}800$ years, which is why it has drifted from Aries into Pisces since the coordinate system was named.
Example
On an equinox the Sun rises due east and sets due west everywhere on Earth, and at solar noon in Charlotte it climbs to $90^\circ - 35^\circ = 55^\circ$ above the southern horizon, exactly halfway between its June height of $78.5^\circ$ and its December height of $31.5^\circ$. The day-length formula $\cos H = -\tan\phi \tan\delta$ has $\delta = 0$ at the equinox, giving $H = 90^\circ$, so geometric daylight works out to exactly $12$ hours at every latitude. Atmospheric refraction adds a few extra minutes on top of that, roughly $5$ minutes at the equator and more at higher latitudes, giving Charlotte closer to $12$ hours $8$ minutes of actual daylight.
Key Insight
The word equinox means "equal night," and it marks the halfway point between the year's longest day and its shortest. Day and night are not perfectly equal on the equinox itself, though: because the atmosphere bends sunlight and sunrise is timed from the Sun's top edge rather than its center, daylight beats night by several minutes, and true equality actually falls a few days before the March equinox and a few days after the September one. What makes the equinox matter most to astronomers is its role as a reference point rather than its equal daylight: the tropical year, the zodiac signs, and the entire right-ascension coordinate grid are all anchored to the moment the Sun crosses the celestial equator.