In the Yeats poem, "The Ballad of Father Gilligan," the fact that half of his flock, half of his parishioners, are lying under green sod is responsible for the priest's exhausted state. The green sod refers to their graves.
Half of his flock is dead, and the father can't keep up. His job is to comfort the dying and administer the last rites. His people are dying so fast that he is exhausted. Even as he dozes off in a chair, he is summoned by another man dying.
The image of the green sod and the graves of his parishioners contributes to the plot of the narrative, explaining and echoing the death of the man who sends to him, as well as explaining why the priest falls asleep and fails to respond to the man's call. This sets up the intervention of God, who sends an angel to take the poor priest's place at the dying man's side.