What is the message of W. B. Yeats' poem "Leda and the Swan"?

If "Leda and the Swan" can truly be said to have a "message," it is perhaps one that can also be identified in another of Yeats's poems, "The Second Coming," in which the "rough beast" of Revelation finds "its hour come round at last." This poem ends as the end of the world begins: in it, an instance has changed everything. In the same way, "Leda and the Swan" is a vivid description of one moment in time that leads to the end of one age and the beginning of a new one.

As detailed in the above answer, the rape of Leda is an occurrence which can be identified as the end of the mythic era and the beginning of modern history: at that moment, we cease to speak of gods and begin a study of the recorded deeds of men. One message of the poem, then, may be that a seemingly insignificant event such as a copulation—"a shudder in the loins," deliberately minimized in importance here by Yeats—can change far more than we could ever anticipate.

We could read other messages into this poem. Its powerful imagery captures the senses: the "blow" and the "great wings beating" make the reader feel their strength. Accordingly, Leda must surrender to the strength of the swan, but also become almost one with it, feeling "that strange heart beating where it lies." The strong is overwhelmingly the stronger of the two, but at the end of the poem, the poet asks whether Leda "put on his knowledge with his power"—that is, did she take into herself the knowledge and power of Zeus when he raped her? This is an interesting idea, suggesting perhaps that, in violating Leda in this way, the god has also surrendered some of his own power. We might infer from this a secondary message that violence diminishes the strong, as well as hurting the victim.

What is the underlying theme of "Leda and the Swan"?

"Leda and the Swan" is written in the style of a Petrarchan sonnet. The first eight lines (octave) describe an event and the final six lines (sestet) resolve the action. Yeats never mentions Zeus or Leda in the poem itself so he was counting on the reader to know the story. Zeus raped (or seduced) Leda, a mortal, while he was in the form of a swan. From that, Helen, Clytemnestra, Castor, and Pollux were born. These were all key players and/or literary characters who took part in events surrounding the Trojan War and the transition from the end of early Greek civilization and the birth of a more modern era. The poem focuses on a particular event, Leda's rape and conception, set to the backdrop of a larger historical transition. The question remaining at the end of the poem is just how much Leda is aware of the significance of her part in this larger historical moment. One very significant theme in this poem is a theory of history. 

The brutality of the event suggests that even as people have relative free will, they are subject to a kind of cosmic (or mythological) force of history. And the other implication is that, cosmic or man-made, historical shifts can be violent. A historical connection to the poem, although not alluded to in the poem, is the Irish Civil War. Yeats supported the Free State of Ireland but did not like the violence that resulted from this struggle for independence. 

An earlier version of the poem was called "Annunciation." This is an obvious reference to the Annunciation in Christianity when Mary was visited by the angel Gabriel who told her she would bear the son of God. The Holy Spirit (in the form of a dove) fulfilled this prophecy. A union between humanity and the divine would be terrifying and would seem so to a mortal more than it would to a God. A clash of civilizations, cultures, or ideas would also be turbulent; historical transitions have often been similarly turbulent. 

In the Annunciation and in Leda's story, the offspring bring a new era of history to the world. Yeats believed in cyclical periods of history. He thought that a dramatic change would occur every two thousand years. During such a dramatic change, things would be disconcerting, turbulent, and possibly violent. This poem symbolizes Yeat's theory of history as it might be understood in natural (physical) and spiritual terms. 

The poem's octave (first 8 lines) describe Leda's rape/seduction. Yeats does not gloss over the violence of the act. So, he notes that violence occurs at historical transitions but by dramatizing the violence, he condemns it, at least as it manifests because of violence in humanity. He ends the poem with the question of whether Leda (or anyone caught up in a historical moment) realizes the significance of the event: 

Being so caught up,
So mastered by the brute blood of the air,
Did she put on his knowledge with his power
Before the indifferent beak could let her drop? 

What is a subtle, less obvious theme in Yeats' "Leda And the Swan"?

"Leda and the Swan" is based on the Greek myth in which Zeus, in the guise of a swan, rapes Leda, who then gives birth to Helen of Troy.  One of Zeus's unfortunate habits was an attraction to mortals, and he often appeared to them as an animal which then raped them  As is not uncommon with acts performed based on raging hormones (lust), there are often unintended consequences of these acts, and in the case of Leda's rape, the consequences are world shaking.

As I noted, Leda gives birth to Helen of Troy, who eventually marries Menelaus, King of Sparta, and after a visit by Hector and Paris of Troy, she either voluntarily goes with, or is simply taken by, Paris.  Menelaus, without sufficient troops to fight a successful war against Troy, seeks and receives Agamemnon's help to assemble a coalition of Greeks to fight Troy and return Helen to Menelaus.

Before Agamemnon commits himself to the war, however, he sacrifices his daughter, Iphigenia, to insure victory, a cold-blooded murder that earns him the hatred of his wife Clytemnestra.  When Agamemnon returns from the Trojan War victorious, his wife and her lover kill him--Clytemnestra has been planning his murder since he sacrificed their daughter.

The Trojan War itself killed tens of thousands of Greek and Trojan troops, most of the Trojan royal family, including Hector's child, essentially wiping away a dynasty that had lasted for hundreds of years and stopped Greek expansion eastward.  Among the Greek dead, of course, were warriors like Achilles and Ajax.  An entire decade was consumed by the war, and even the victors--Odysseus and Aeneas, for example--continued to pay for the war long after its conclusion.

When Zeus gave in to his lust for Leda, it is unlikely that he thought about the obvious consequence of his actions, the birth of a child, but the unrecognized and unintended consequences essentially shifted the balance of power between Greece and Troy to Greece, and Troy is remembered only as the subject of a poem.