There are many examples of symbolism in the poem. Remember that Yeats is writing this as the First World War has ended. Its shattering of Europe both physically and morally has left permanent scars on both landscape and people. At the same time, Yeats possesses this unshakable feeling that it's not over, that something more sinister looms on the horizon. The use of symbols in the poem helps to convey both. The opening image of the "widening gyre" brings forth the idea that a vortex of some type, a black hole has descended upon humanity. This lack of clarity and uncertainty is why the normally reliable "falcon cannot hear the falconer." The idea of the center being unable to hold as "things fall apart" is another symbolic image which brings forth the idea that the political and moral structure that guided people has been broken and all that is left is the presence of "mere anarchy." There is little certain in this setting other than "the best lack all conviction and the worst are filled with passionate intensity." These symbols in the opening stanza go very far in representing a world that is left with little in way of hope and redemption.
The symbolism of "The Second Coming" is the Christian belief that the reappearance of Christ is what will put right all that is wrong. It is the moment of human absolution, and this vision of totality is addressed in the poem. While Yeats open with a call that "some revelation is at hand," he also symbolizes this with a description of a rather horrific figure, which is meant to symbolize how individuals are prone to embrace nearly anything that might be disguised or concealed as hope even if it symbolizes the exact opposite of it. The symbolism of this image acquires even greater significance when seen in the emergence of dictators like Hitler, Stalin, Fanco, and Mussolini throughout Europe. As this figure, once seen to be symbolic of the Second Coming comes into view, the symbolism of it slouching "towards Bethlehem, waiting to be born" brings for the image of not a triumphant vision, but rather one that terrifies and strikes at the very essence of who we are and in what we believe. This ultimate act of symbolism helps to bring forth the idea that we, as individuals, wait for something to not save us, but actually terrify us more.