In "Byzantium," Yeats explores the relative superficiality of life in contrast to the permanence of art, which, unlike life, endures.
Yeats invites us to enter into the ancient city of Byzantium at night, where everything that is human—symbolized by the drunken, sleepy soldiers—has retreated into the darkness, whereas the great objects of art and architecture live on, epitomized by the "starlit or moonlit dome" that disdains everything man is.
The dome can do this because it represents all that is permanent and eternal, whereas "The fury and the mire of human veins" highlight the inherent ephemerality of the life of man.
Paradoxically, the great works of art and architecture that Yeats finds so utterly beguiling were created by mortal men. Those men will die, but their creations will live on to enthrall and captivate successive generations. Human handiwork, as embodied in the beautiful golden metal bird in the third stanza, achieves a state of immortality that humans themselves can never achieve.
The contrast between spirit and matter, between the eternal and the fleeting, is brought before us once more in the final stanza, where spirits ride upon dolphins, with their "mire and blood."
The spirits will continue to travel to the next world—for which Byzantium stands as a metaphor—despite their needing to travel through a "dolphin-torn ... gong-tormented sea," which perhaps one might see as a metaphor for a process of purification.