The point in the Earth's orbit where the apparent declination of the Sun is zero: the Sun is at its zenith at the terrestrial equator. The equinox is the point of intersection of the ecliptic (the apparent trajectory of the Sun in the celestial sphere) and the Earth's equator.
The spring (20, 21 or 22 March, in the northern hemisphere) and autumn equinoxes (21, 22 or 23 September in the northern hemisphere) are the dates when the day and night have equal durations, which explains the etymology of the term.
In the southern hemisphere the dates are inverted.
The equinoxial line is the intersection of the ecliptic plane and the celestial equator. The solstice axis is perpendicular to it. The intersection corresponding to the spring equinox is the vernal point, and serves as a reference for celestial longitudes and right ascensions.
The precession of the equinoxial line, discovered in the 2nd century BC by Hipparcus of Nicaea, is a retrograde movement of these points, making them describe an elliptic in 25 800 years. This movement causes the difference of twenty minutes between the tropical year (the duration between two spring equinoxes) and the sidereal year (the time for the Earth to make one revolution of the Sun).