A reference to one of the twin eggs of Leda and Zeus disguised as a swan from which Helen was born. Had Leda not laid the egg, Helen would not have been born, so Paris could not have eloped with her, so there would have been no Trojan War etc. The English use of the phrase comes from Horace's De Arte Poetica

Nec gemino jusque ad mala

(From the egg to the apples)

Which refers to the Roman repast which began with an egg, and finished with apples.