"At a Potato Digging" is written from third-person perspective - someone uninvolved with the action is describing what is happening. A mechanized digging machine is unearthing potatoes, which human workers are then collecting.
Much of the appreciation of the poem stems from understanding Irish history and how integral the potato is to the Irish diet. The third stanza of the poem refers to the Potato Famine, a period from 1845-1852 when a disease called potato blight affected the harvests. "Live skulls, blind-eyed, balanced on wild higgledy skeletons" describes the starving people who "wolfed the blighted root and died." The famine, and the huge drop in population as a result of the deaths and of the emigration out of Ireland of many others, is a critical event in the history of Ireland.
As the first, second, and fourth stanzas celebrate, the potato harvest at the digging being described is plentiful. The workers give thanks as "heads bow" and they toil on "humbled knees" to gather the "knots of potatoes...whose wet inside promises taste of ground and root."
Religious references are scattered throughout the poem. The harvest-workers engage in "processional stooping" such as happens in the Catholic Church upon entering and walking toward the altar' in this case, they are paying "homage to the famine god" at the "seasonal altar of the sod." The rotted potatoes are described as having spent "three days in the long clay pit," a reference to the three days Jesus spent in the cave.
In the first and last stanzas, a simple abab rhyming pattern is followed by each set of four lines. The third from the last and final lines of the two sections of the second stanza rhyme, while the other lines are free verse. In the third stanza, the first two lines are unrhymed but the last two lines do rhyme in each quatrain.