Byzantium (that is, Constantinople or Istambul) was the capital of Eastern Roman Empire, an empire of Hellenic Christian culture which lasted from the third century AD to the fifteenth. Yeats knew of the Byzantine civilization mainly through reading. In the poem Sailing to Byzantium, Byzantium stands large for the permanence of art and thought as against the transience of mere animal life.
In the first stanza Yeats, describes the natural world where the young of all species – birds, fish, people – are busy, loving, reproducing, that is, the drear fulfilling of conjugal duty, and approving the flesh. These "dying generations" being caught in the "sensual music" of life, neglect works of art, religion or philosophy which are "monuments of unageing intellect". Among the young sensualists, there is obviously no place for an aged man like Yeats, which senses have already begun to fail.
In the second stanza, Yeats describes his old age predicament. He is no more than a scarecrow, a "tattered coat up a stick," and he will remain so unless he rejects the flesh and concentrates on improving his soul by learning to sing. Unlike the "sensual music" of the natural world, there is also a spiritual music which the soul can study – the music of art and of poetry, for instance. Indeed poems are monuments of the soul's magnificence. It is on this spiritual quest that he has mentally sailed the seas and come to the holy city of Byzantium.
In the third stanza, Yeats addresses the "sages standing in God's holy fire," pictured in the gold mosaic of the walls of the churches, to come from the holy purgatorial fire and spiral down to where he is,
Sick with desire
And fastened to a dying animal.
He wants them to burn away his heart, obsessed with its flesh mortal dreams, and to teach him how to sing – teach him the secrets of the soul and of art, of the "artifice of eternity." This immortality is heaven-like goal of art, where the artist's creativity and God's creation become one or where the artist himself becomes the artifact, object d'art that is, the very work of art.
Having rejected the natural world's sensuous music he himself the golden singing bird, supernaturally wise, who sings the soul's music – the knowledge of all the ages – to the Emperor and the mythical lords and ladies of Byzantium.