This poem charts the struggle that Heaney has as he seeks to be true to his cultural heritage and family background whilst at the same time finding that he is a very different kind of person from his father and grandfather. He finds himself particularly ill-equipped to dig in the same way as his father and grandfather do.
However, by the end of this poem, that could be considered an evocation of rural Irish life, Heaney discovers that his skill as a writer and a poet allows him to metaphorically "dig" as he seeks to discuss and present Ireland and his background through his art:
Between my finger and my thumb
The squat pen rests.
I'll dig with it.
The diggers in this poem are therefore the speaker, his father and his grandfather, who all, in their different ways, dig in their lives using different implements but with the same results.