In "Elegy Written in a Country Churchyard," what has prevented the villagers from achieving greatness?

Gray's "Elegy" is one of the major lyrics of the eighteenth century, and one of the representative poems of the "graveyard school" of poetry, a major theme of which was the need for living a sensible, good life in view of the inevitability of death. As a biographical note, you might point out that Gray himself was the only one of his parents' twelve children to grow to adulthood. A concern with death and how to take life is therefore not an unexpected aspect of his art.

The setting of day of the poem is twilight. The cattle are heading back to the barn to be milked, the farmer is returning from the fields, the sun is setting, and the curfew bell is ringing from the church tower. For much of the poem, the speaker seems to be addressing no one in particular, but in line 37 he does address “yeproud,” and in line 93 he seems to speak to a person who is buried in the country churchyard. 

The people buried in the church graveyard are humble, rural folk. Yet the speaker asserts that they are not contemptible because of their simplicity; instead he emphasizes their “useful toil” and “homely joys,” pointing out that death is the great leveler, and that “the paths of glory lead but to the grave” (one of the more famous lines of English literature). Some of those buried here might have made great rulers, musicians, defenders of human rights, or poets. But the speaker balances the missed opportunities for good that are buried here by pointing out that the people never had the chance to do evil either. In short, the churchyard is the occasion of reflection on the need for goodness and piety, and the inevitability of death is cause for people to live their lives to their fullest potential.