The poem begins with the image of a falcon flying out of earshot from its human master. In medieval times, people would use falcons or hawks to track down animals at ground level. In this image, however, the falcon has gotten itself lost by flying too far away, which we can read as a reference to the collapse of traditional social arrangements in Europe at the time Yeats was writing.
In the fourth line, the poem abruptly shifts into a description of "anarchy" and an orgy of violence in which "the ceremony of innocence is drowned." The speaker laments that only bad people seem to have any enthusiasm nowadays.
At line 9, the second stanza of the poem begins by setting up a new vision. The speaker takes the violence which has engulfed society as a sign that "the Second Coming is at hand." He imagines a sphinx in the desert, and we are meant to think that this mythical animal, rather than Christ, is what is coming to fulfill the prophecy from the Biblical Book of Revelation. At line 18, the vision ends as "darkness drops again," but the speaker remains troubled.
Finally, at the end of the poem, the speaker asks a rhetorical question which really amounts to a prophecy that the beast is on its way to Bethlehem, the birthplace of Christ, to be born into the world.