Analysis: What's Up With the Title?
When Yeats wrote this poem in 1928, most of his readers would have been familiar with the story of Leda and the Swan. Nowadays, it helps to have a good online encyclopedia to help out with references to Greek mythology.
Without digging too far into Greek mythology, all you need to know is that Leda was a girl from Ancient Greece who was raped (some versions of the story say seduced) by the Zeus, the head of the Greek gods, disguised as a graceful swan. As a result of the encounter, Leda gave birth to Helen of Troy, who would have won People magazine's "Most Beautiful Person of All Time" award, if they had People back in the day. Leda also gave birth to the twin warriors Castor and Pollux. And these kiddies were hatched from eggs (or at least some of them were, depending of which version of the story you're reading).
The Trojan War was fought over Helen, who was lawfully married to a Greek king before being abducted (perhaps willingly) by a Trojan prince. Helen's husband said, "This means war!" and so it was. The Trojan War was the major topic of Homer's Iliad.
That's pretty much the bare bones of the story that Yeats wants to raise with the title. And it's a good thing he gives us this title, because otherwise we'd have no idea who or what he was talking about. We'd think that he had written an erotic poem set in an aviary, or bird zoo.
The title also raises a whole host of associations from the history of western art. The story of Leda and the Swan was too tantalizing for many artists to resist, and it has been represented in countless sculptures and paintings. The challenge for these artists was to come up with a new and original perspective on the story, and that was Yeats's challenge, too. In particular, the story has not been told as frequently in words as in images.