According to Wikipedia: The precise origin of the ancient custom of decorating eggs is not known, although evidently the blooming of many flowers in spring coincides with the use of the fertility symbol of eggs—and eggs boiled with some flowers change their color, bringing the spring into the homes. Many Christians of the Eastern Orthodox Church to this day typically dye their Easter eggs red, the color of blood, in recognition of the blood of the sacrificed Christ (and, of the renewal of life in springtime). Some also use the color green, in honor of the new foliage emerging after the long dead time of winter.
According to a certain editor, he believes that the connection between eggs and Easter is the fact that they represent fertility and restoration. Eggs are seen as restoration, which came with the spring.