Anna Laetitia Barbauld learned Latin, Greek, French, and Italian from her father, a dissenting academy teacher—unusual for women in 1770s England. Her 1773 debut Poems was praised specifically for its classical learning. This piece appears in that collection.
By opening with untranslated Virgil, Barbauld demonstrates literacy that most of her female readers wouldn't share—but that male critics demanded as proof of "serious" poetry. The gesture is simultaneously exclusive (you need Latin) and defiant (women can have Latin too).
The choice of this particular passage is pointed. Virgil's shepherd claims his "slender" basket-weaving song is enough for the goddesses—the Muses. Barbauld, weaving her own fiscellam (little basket) of poems, makes the same claim. But where Corydon's modesty is undercut by his actual eloquence, Barbauld's is undercut by her refusal to translate or explain. The poem says "this is enough" while doing something quite assertive: claiming Virgil's voice as her own.