The falcon
The falcon, which has become separated from the falconer, likely represents humanity itself, which has become detached from its God, or from once-revered standards of morality and order.
The falconer
The falconer may represent God, or it may represent traditional values, ethical responsibility, and order that was once in control of the falcon. The Second Coming, whatever exactly it may be, has shattered the falconer's (ruler's) contact with the falcon (ruled), leaving both stranded and alone.
The sphinx
The phrase "shape with a lion body and a head of a man" describes a sphinx, a mythological creature that often guards the entrance to hidden treasures in ancient myths. Sphinxes are known for being cruel tricksters, and in many myths, sphinxes ask those trying to pass by to solve riddles; they devour those who cannot answer correctly. In "The Second Coming," the sphinx marks the narrator's riddle-laden entrance into a nightmarish vision of the future, which he accesses through the liminal, dreamlike space of the poem.
The rough beast
The "rough beast," the thing "Slouching towards Bethlehem to be born," is a force that will define the entirety of the aftermath of the Second Coming. It most likely represents a dark, chaotic, unpredictable future, but its arrival could also hint at changes that could lead to new possibilities.
The speaker
The poem has a speaker, referred to as "I" in the fifth-to-last line. Most likely this speaker is Yeats. The "I" also may be a stand-in for the reader of the poem, or for anyone affected by the onslaught of modernity and the chaos of the 20th century.