We see three generations of men from the same family in "Digging." The speaker is the youngest, and he reflects on his father and grandfather. We see the similarities through the generations (they all work hard, and value hard work), and the differences (the speaker has chosen an entirely different line of work from his father and grandfather). Plus the speaker compares himself to the men who came before him; he knows he's breaking family tradition by becoming a writer instead of a man who works the land, and that makes him a wee bit uncomfortable. Farming is a huge part of his family's identity, so our speaker has to figure out how he fits into a family where he carries out an entirely different role.
The speaker has never had a close relationship with the men in his family, and that's why he feels like even more of an outsider for not working the land.
Although the speaker has chosen a different line of work from his father and grandfather, he still feels connected to them through the hard work and skill required of a writer.