In the southern hemisphere, the equinox occurs at the same moment, but at the beginning of spring. There are two conventions for dealing with this: either the name of the equinox can be changed to the vernal equinox, or (apparently more commonly) the name is unchanged and it is accepted that it is out of synch with the season.
At the equinox, the sun rises directly in the east and sets directly in the west. In the northern hemisphere, before the autumnal equinox, the sun rises and sets more and more to the north, and afterwards, it rises and sets more and more to the south.
This is when the NeopaganSabbat of Mabon is celebrated. Also, Autumnal Equinox Day (秋分の日) is an official national holiday in Japan, and is spent visiting family graves, and holding family reunions.
In the cycle of manifestation of, say, an idea, the AutumnEquinox is point where the idea has become manifest, has grown through fertilization and the nurturing of Mother Nature, and is now more than ready for harvest.
Equinox means "equal night," and anywhere on the Earth, given a level horizon, the Sun rises due East, and sets due West.
The AutumnEquinox is one of the Four Quarter Days of the year.