How are the first days of winter and summer chosen?

Summer TimeThe Imponderable was posed by a called on John Dayle’s radio show in Cleveland, Ohio.  John and the supposed Master of Imponderability looked at each other with blank expressions.  Neither one of us had the slightest idea what the answer was.  What did it signify?

We received a wonderful answer from Jeff Kanipe, an associate editor at Astonomy. His answer is complicated but clear, clearer than we could rephrase. So Jeff generously has consented to let us quote him in full:
The first day of winter and summer depend on when the sun reaches its greatest angular distance north and south of the celestial equator.
Imagine for a moment that the Earth is reduced to a tiny ball floating in the middle of a transparent sphere and that we’re on the “outside” looking in.  This sphere, upon which the stars seem fixed and around which the moon, planets, and sun seem to move, is called the celestial sphere.  If we simply extend the earth’s equator to the celestial sphere it forms a great circle in the sky: the celestial equator.
Now imagine that you’re back on the Earth looking out toward the celestial sphere.  You can almost visualize the celestial equator against the sky.  It forms a great arc that rises above the eastern horizon, extends above the southern horizon, and bends back down to the western horizon.
But the sun doesn’t move along the celestial equator.  If it did, we’d have on eternal season.  Rather the seasons are caused because the Earth’s pole is tilted slightly over 23 degrees from the “straight up” position in the plane of the solar system.  Thus, for several months, one hemisphere tilts toward the sun while the other tilts away. The sun’s apparent annual path in the sky forms yet another great circle in the sky called the ecliptic, which, not surprisingly, is inclined a little over 23 degrees to the celestial equator.
Motions in the solar system run like clockwork.  Astronomers can easily predict (to the minute and second!) when the sun will reach its greatest angular distance north of the celestial equator.  This day usually occurs about June 21. If you live in the Northern Hemisphere and note the sun’s position at noon on this day, you’ll see that it’s very high in the sky because it’s as far north as it will go.  The days are longer and the nights are shorter in the Northern Hemisphere.  The sun is thus higher in the sky with respect to our horizon, and remains above the horizon for a longer period than it does during the winter months.  Conditions are reversed in the Southern Hemisphere: short days, long nights. It’s winter there.
Just reverse the conditions on December 22.  In the Northern Hemisphere, the sun has moved as far south as it will go.  The days are short, while the lucky folks in the Southern Hemisphere are basking in the long, hot, sunny days.
The first days of spring and fall mark the vernal and autumn equinox, when the sun crosses the equator traveling north and south.  As astronomer Alan M. MacRobert points out, the seasonal divisions are rather arbitrary:
Because climate conditions change continuously, there is no real reason to have four seasons instead of some other number.  Some cultures recognize three: winter, growing and harvest.  When I lived in northern Vermont, people spoke of six: winter, mud, spring, summer, fall and freezeup.

From: When Do Fish Sleep? by David Feldman