The day and night are not equal on the equinox, though they are about equal. Equinox is when the Earth's axis is not tilted towards the sun, or equivalently the path of the sun passes from the Northern to the Southern hemisphere.
Sunrise and sunset are measured from the "top" of the sun, not the centre, and the refraction of the atmosphere means that the sun is visible from the surface, even after it would have set were there no air to bend its light. Finally the Earth's elliptical orbit also varies the length of the day.
The day on which the day and night are equal varies with latitude. In Boston, at 42 degrees North (it's as far south as the French Riviera - always surprises me) the day is 12 hours long on Sept. 26.
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