William Butler Yeats's line—part of which would inspire the title of Chinua Achebe's novel Things Fall Apart—speaks to the First World War's disruption of previously held, self-evident truths. Ideas about morality, identity, and social roles changed radically. The war led to old empires, which had already been crumbling, falling apart—particularly the Austro-Hungarian Empire. It was the assassination of the Archduke Franz Ferdinand by the Serbian Gavrilo Princip which acted as the catalyst for the war.
Moreover, some of the conditions of President Woodrow Wilson's Fourteen Points required certain European countries to give up certain colonial holdings and to redraw borders within the continent in a way that respected the autonomy of certain ethnic groups.
The "center" that had previously held nations and peoples together could no longer "hold." This disillusionment with postwar life was best reflected in the visual art and literature of the time, which sought new modes of seeing the world and of describing its conditions, due to previous models no longer being sufficiently expressive.
With this line, Yeats was suggesting that the foundations of Western culture, in particular Christianity, were falling apart. In the wake of the First World War and the Bolshevik Revolution, European society was experiencing extreme social, cultural, and political unrest. Yeats sees in this unrest the end of a historical cycle, one which had seen the rise, and, he thought, the fall, of Western civilization. After the "center" collapsed, "mere anarchy" would be loosed upon the world, to be replaced, ultimately, with something that Yeats fears, a "rough beast" that "slouches toward Jerusalem." Particularly in the passage in question, Yeats is evoking apocalyptic images, but he is not suggesting that the new era ushered in will be the Second Coming of Christ, but the birth of something new and frightening.