The widening gyre (symbol)
"Gyre" is actually a scientific term used to refer to a vortex located over the air or sea, and it usually refers to systems of circulating ocean currents. In Yeats's "The Second Coming," "gyre" is used to represent the swirling, turning landscape of life itself.
Gyres apper in many of Yeats's poems. He uses it to represent the systems that make up life, the push-pulls between freedom and control that spin together to create existence.
The falcon (symbol)
The falcon, separated from the falconer, is lost: without reason, without ruler, without larger cause. It is a symbol for a lost humanity, at the mercy of uncontrollable forces. The falcon, in short, is all of us, wandering around the earth, trying to find meaning.
The falconer (symbol)
The falconer is a symbol that may represent God, or a wider standard of ethics or morality.
The blood-dimmed tide (symbol)
The blood-dimmed tide, loosed upon the world, is a symbol that represents overwhelming violence and uncontrollable chaos.
The sphinx (symbol)
The sphinx, perhaps, represents the bearer of the riddle-like prophecies that the narrator is trying to unwind, the creature in between the narrator and the answers he is looking for. He is mystified by what has been happening around him, but he believes that it is not all accidental, and he is trying to find clues in the seemingly inexplicable events that have been occurring around him. In mythology, sphinxes often delivered riddles and would sometimes kill those who could not answer the riddle. Perhaps this sphinx is asking what the poem is asking—what rough beast is emerging? What is this nebulous world called the future going to look like?