It might not seem like it at first glance, but Heaney is actually being quite creative with the title of this poem. On the one hand, we discover pretty quickly that the poem will literally be about digging – for flowers, potatoes, and peat. But we soon find out that there are other, less literal meanings, and we'll have to do a little digging ourselves just to figure them out.
For example, the speaker is a writer, so digging could refer to the kind of investigating and soul-searching writing involves. The speaker also spends tons of time digging into his past. He even talks about roots and his family's history. So while the title may appear straightforward at first, it takes on multiple meanings the more we, well, dig into it.