According to legend, the one day a year you can stand eggs on end
is March 21, the first day of spring, also known as the "vernal
equinox". On the vernal equinox, day and night are the same
length, and the sun passes directly over the earth's equator. A
few folks got the idea this meant the force of gravity was put in
balance somehow, making it easier to balance eggs.

Well, here's a news flash: You can stand eggs on end any 'old
time', not just on the vernal equinox. All you need are steady
hands and a lot of patience. Also, it wouldn't hurt to have about
a dozen eggs. (Some are flatter on the bottom than others.) Our
method is to concentrate, try mil hard, and if at first you don't
succeed, give up. No sense killing yourself over a stupid egg.
Besides, the next one in the box may be easier.
It helps if you shake the egg up first, by the way. That breaks
loose the yolk. Normally, the yolk hangs in the center of the egg
from two bands called "chalazae" (they're the white stringy
things you sometimes see attached to the yolk when you break the
egg). Break the chalazae and the yolk sinks to the bottom. That
makes the egg bottom heavy and easier to stand up. It's also
cheating. But if the audience is waiting and your reputation is
on the line... well, let your conscience be your guide.

~source used: "Know It All"
by Ed Zotti

According to a legend, Christopher Coumbus challenged the Spanish court to stand an egg on end when they thought anyone could have duplicated his feat. He then showed them how to stand the egg when they failed, thus proving to them that things are easiest when someone shows you how to do them. From this we get the expression, "Columbus' egg" for something we realize we should figured out for ourselves but had to have someone else point out to us.

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