Expressing our emotions through the shedding of tears is an ancient gesture, one that goes back to the dawn of civilization. For the purposes of the poem, however, Edna St. Vincent Millay goes back thousands of years to the mythological world of Homer, where Penelope, wife of the hero Ulysses, cried as she waited for her husband to return to Ithaca.
Penelope's was a truly heartfelt gesture, a genuine expression of her emotions. Rather like the speaker herself, who dabs her moistened eyes on the corner of her apron, Penelope routinely burst into tears in the absence of her husband.
Ulysses also knew how to cry, but he learned it from Penelope, an indication that shedding tears is more authentically feminine, that it comes more naturally to women than men, who have to learn it from their wives and mothers. Ulysses's tears, like those of Penelope, were an ancient gesture, but because this gesture was learned rather than coming naturally, it lacks a certain something in authenticity.
The speaker cites Penelope as a kind of universal representation of womanhood. It is this very universality that allows her to make a connection between herself and her sad predicament with that of a queen from ancient mythology, crying and weaving—and unweaving—as she waits for her husband to come home.