This poem begins with a description of Cadmus and Harmonia, two mythological characters who were turned to snakes. (See the Analysis for their backstory).
The snakes live in peace and tranquility on the sunny shores of the Adriatic Sea. After everything they suffered, they no longer have to face the struggles of their unhappy, old home. At first, they had sat helpless at home, watching a curse befall their children and calamity overtake their city.
However, as serpents, they can escape both the world and their sorrows, and hence now live happily, having "wholly forgotten their first sad life."
This poem relying on an allusion to the myth of Cadmus and Harmonia, it is important to know that story. In Greek mythology, Cadmus of Thebes carried off and married the goddess Harmonia. She later left Thebes with him, and they together assisted the Encheleans in their war agains the Illyrians. Though they succeeded and Cadmus was named king of the Illyrians, he was later turned into a serpent. To assuage Harmonia's grief over his condition, the gods turned her into a serpent as well.
Where that story has a bittersweet element in its end, Arnold reinterprets their fate, arguing that their escape from society and their former lives provided them with happiness that they never could have achieved while managing the world of men. This argument aligns with the poet's own perspective, from which he regularly criticizes the modern world and its limitations on the poetic instinct. Arnold frequently suggests that man can reach his best self by focusing on nature, and so sees in his title characters' fate a blessing. Of course, because he cannot himself achieve such transcendence, his admiration has its own bittersweet tinge. As he usually does, he admires the potential for humans to improve through nature, but laments their seeming inability to do so for very long.
Harmonia's name, purpose, and presence in this poem aligns with its theme as well. Obviously, her name means harmony, a word often associated with peace and agreement. She was the Greek goddess of harmony and concord, but she was only able to achieve the tranquility her name suggests after being turned into a serpent and leaving Thebes. Even as a deity, she could not reach serenity while in a human form. Desires weighed her down until she lost that body.
As in many of his poems, Arnold's choice metaphors for peace, tranquility, and prosperity all come from natural settings. The rolling Adriatic Sea plays a large role in this poem, as do grass, flowers, sand, and sun. The contrast between this natural setting and the populated city of Thebes is very prominent. Since cities offer the most obvious representations of modern life, it makes sense that Arnold would continuously condemn them. Cadmus and Harmonia left behind cities and war for serenity and nature, and in Arnold's mind, this benefited them more than anything else.