The two lines occur at the end of the third stanza in Andrew Marvell’s poem “The Garden.” Before this couplet, Marvell calls out “lovers” who “cut” (write) the names of their mistresses into trees. These people aren’t presented as cultivated or mindful. In Marvell’s opinion, there is not a lover in the world who possesses the beauty of a tree. Marvell doubles down on the allure of trees when he addresses them directly. “Fair trees!” he proclaims. Fair was once a common way to call someone or something beautiful.
Marvell has something specific that he wants these attractive trees to understand. He makes a promise to the trees. He tells them, “wheres’e’er your barks I wound, / No name shall but your own be found.” In other words, if Marvell should ever feel the urge to carve (“wound”) a name into the bark of a tree, it would be the name of that tree, not the name of a mistress or a romantic partner.
Marvell's attitude juxtaposes that of the human lovers alluded to earlier. The lines symbolize Marvell’s devotion to nature and trees. Marvell can’t literally carve the tree’s name into the tree because trees don’t tend to talk or carry proper human names. However, figuratively speaking, the gesture makes sense, as it reinforces Marvell’s faithfulness. There is nothing more becoming and pleasing than a tree, which is why Marvell treats them like a great love.