The legend appears to stem from a "seasonal gravity." Unlike Dec. 21 when the Earth's tilt has us pointed away from the sun, and June 21 is when we're tilted the most toward the sun, the equinox dates are when we're exactly in between, and the Earth's tilt is at a 90 degree angle with respect to the sun's light.
Some felt that meant the Earth's tilt is zero then, and so with the Earth pointing straight up, that eggs will stand up and not be pulled over by the tilt.
But it's all wrong. The equinox just means equal daylight on the planet, and gravity and our tilt is always the same. You can stand an egg on any date -- go try it now!
The article below from Phil Plait's "Bad Astronomy" Page has some great explanations on this and much more explanation.
For More Information