That twenty centuries of stony sleep were vexed to nightmare by a rocking cradle, and what rough beast, its hour come round at last, slouches towards bethlehem to be born? in the excerpt above, “twenty centuries” is a reference to the fall of the roman empire christianity feudalism the british empire

Explanation:

The author portrays a nightmarish scene: the bird of prey, turning in a broadening "gyre" (winding), can't hear the falconer; "Things go into disrepair; the inside can't hold"; turmoil is loosed upon the world; "The blood-darkened tide is loosed, and wherever/The service of honesty is suffocated." The best individuals, the speaker says, do not have all conviction, yet the most noticeably bad "are loaded with enthusiastic power."  

Without a doubt, the speaker affirms, the world is close to a disclosure; "Most likely the Second Coming is within reach." No sooner does he think about "the Second Coming," at that point he is harried by "a huge picture of the Spiritus Mundi, or the aggregate soul of humanity: some place in the desert, a monster sphinx ("A shape with lion body and the leader of a man,/A look as clear and barbarous as the sun") is moving, while the shadows of desert winged animals reel about it. The obscurity drops again over the speaker's sight, yet he knows that the sphinx’s twenty centuries of “stony sleep” have been made a nightmare by the motions of “a rocking cradle.” And what “rough beast,” he wonders, “its hour come round at last, / Slouches towards Bethlehem to be born?”