Many people like to stand an egg on its end on the first day of spring (the vernal equinox) because they think it's the only time of the year it can be done. The claim is that the earth and sun are perfectly aligned and the earth's rotation is just right for an egg to stand on it's end. The first day of fall (the autumnal equinox) sees similar daylight lengths as the first day of spring. Plus, eggs are covered with bumps and indentions that will allow one egg to stand easier than another one.
The legend of standing eggs on their end comes from China, where it's a ritual of the beginning of spring--celebrated about 6 weeks before the vernal equinox (many cultures celebrate spring's arrival before the actual date of the vernal equinox). A magazine reporter in China in 1945 reported this tradition and that's how the legend made it's way to America.
For more info on the web on the egg-balancing myth, visit the following:
from the Urban Legends Reference Page