Here's a take on the obvious answer. (I highly recommend Matt Throwers answer providing a supportable interpretation in an alternate framework. Also Mozibur Ullah's answer, which shows that the symbols can have a range of meanings, without undermining the poem's intent.)
- The Falconer is the Redeemer, the falcon the human spirit
Birds have long been used as a symbol of the spirit, but this is an astonishing choice. Yeats forces us to regard the paradigm in a fearsome form, not lambs and shepherd, but as hunter and bird of prey. In Blake's most famous poem, he asks of the Tyger: "Did he who made the lamb make thee?", and, later, C.S. Lewis uses a lion (Aslan) as the Christ figure.
Yeats' is a deep metaphor because here we have a relationship where the benefactor (the falconer) sends the ward into the world seeking nourishment. This must be understood in the context of spiritual nourishment, because the falcon brings it home to share with the benefactor. If the falcon goes so far afield that it cannot return, it can't share the nourishment with the benefactor--potentially the nourishment is no longer spiritual, but merely material.
Note that Eliot will later refer to
"the spirit unappeased and peregrine"
The choice of the falcon may also refer to the spirit of inquiry that begins with humanism and the Ancient Greeks ("5th Century" Athens in particular) and leads to the Renaissance and the Enlightenment. Second Coming was largely a response to the horrors of World War I, but the 20th Century, even in the first decades, was also a century of wonders.
But that spirit of inquiry, which soars to unimagined heights, also can be said to have lead humanity astray. Nietzsche stated that god was dead. One of Yeats' responses is that god is continually slain and reborn:
I saw a staring virgin stand
Where holy Dionysus died,
And tear the heart out of his side,
And lay the heart upon her hand
And bear that beating heart away;
And then did all the Muses sing
Of Magnus Annus at the spring,
As though God’s death were but a play.
Another Troy must rise and set,
Another lineage feed the crow,
Another Argo’s painted prow
Drive to a flashier bauble yet.
The Roman Empire stood appalled:
It dropped the reins of peace and war
When that fierce virgin and her Star
Out of the fabulous darkness called.
Two Songs from a Play Full text of The Resurrection (1931)
Here Yeats is at once referring to Virgo and Spica (Kore as the female analogue of Dionysus) and the virgin Mary and the star of Bethlehem. He reveals, under the Greek conception, the origin of poetry in religion. (The Festival of Dionysus was a religious festival.)
"Fabulous darkness" is likewise the most brilliant possible choice--fabulous derives from the Latin word for story (fabula), which conjures an image of a cornucopia of light generated from the darkness. In some sense, stories are all we have—not only do we put our faith in them, it is from the miraculous they emerge. Here is it the death of God specifically that inspires the Muses to sing.
The second song also comments on Second Coming:
In pity for man’s darkening thought
He walked that room and issued thence
In Galilean turbulence;
The Babylonian starlight brought
A fabulous, formless darkness in;
Odour of blood when Christ was slain
Made all Platonic tolerance vain
And vain all Doric discipline.
Everything that man esteems
Endures a moment or a day.
Love’s pleasure drives his love away,
The painter’s brush consumes his dreams;
The herald’s cry, the soldier’s tread
Exhaust his glory and his might:
Whatever flames upon the night
Man’s own resinous heart has fed.
The vocabulary is incredibly precise, with words such as "pity" (see the Pietà). These verses are have high information density, and layers of meaning, but "man's own resinous heart" seems a good place to leave things.
Yeats clearly regards the Bethlehem story in the greater context of Greek mythology, but this is in no way a repudiation. On the contrary, Yeats' connects it to something even older, and affirms the eternal nature of the cycle, here in the partly context of that which inspires mankind--poetry and stories.
One of the meanings that can be drawn from the play The Resurrection is the response to the miracle. The promise of eternal salvation quickly devolves into a death cult which venerates suffering.
Shakespeare and Birds of Prey
Here's a fun site I found "Shakespeare's Swooping Imagery" with a few salient excerpts:
Hist! Romeo, hist! O, for a falconer's voice,
To lure this tassel-gentle back again!
Bondage is hoarse, and may not speak aloud;
Else would I tear the cave where Echo lies,
And make her airy tongue more hoarse than mine,
With repetition of my Romeo's name.
(Romeo and Juliet, Act II, Scene 2)
Note that this derives from that most famous of scenes which begins with "But, soft! what light through yonder window breaks?" and the subject is love.
My falcon now is sharp and passing empty.
And till she stoop she must not be full-gorg'd,
For then she never looks upon her lure.
Taming of the Shrew, Act IV, Scene 1
Here, Petruchio is referring to Kate, the object of his love. The Dauphin in Henry V also uses the metaphor, describing the feeling of riding his steed:
When I bestride him I soar, I am a hawk.
Henry V, Act III, Scene 7
There is also the dark side:
Look, as the full-fed hound or gorg'd hawk,
Unapt for tender smell or speedy flight,
Make slow pursuit, or altogether balk
The prey wherein by nature they delight;
So surfeit-taking Tarquin fares this night:
His taste delicious, in digestion souring,
Devours his will, that lived by foul devouring.
The Rape of Lucrece, 694-697
This said, he shakes aloft his Roman blade,
Which, like a falcon towering in the skies,
Coucheth the fowl below with his wings' shade,
Whose crooked beak threats if he mount he dies:
So under his insulting falchion lies
Harmless Lucretia, marking what he tells
With trembling fear, as fowl hear falcon's bells.
The spiritual decay Yeats writes of is embodied in Tarquin. Measure for Measure comments more directly:
This outward-sainted deputy—
Whose settled visage and deliberate word
Nips youth i' th' head and follies doth enmew
As falcon doth the fowl—is yet a devil.
His filth within being cast, he would appear
A pond as deep as hell.
Measure for Measure, Act III, Scene 1