The poem opens with the speaker's father plowing in the fields. He seems pretty darn good at it, too. He leads his powerful horses through the field with grace, and Heaney describes the taxing nature of the work.
The young speaker follows his father as he works, but he's nowhere near as comfortable with the task. He's clumsy, and often stumbles and falls trying to keep up with the father-horse duo. The speaker talks about how he looked up to his dad, and wanted to grow up to plow too, but how he was never skilled enough to make it happen, which seems like kind of a bummer until we realize that the speaker turns out perfectly alright.
At the end of the poem, we're sped up to the present day, where, in a complete turn of events, the elderly father is now following the grown-up son, just as the son used to follow in his father's wake while he was plowing the fields. It's a complete one-eighty, and shows that, although the speaker was kind of a dud when it came to farming, that he turned out to be his own person and now his father actually looks to him for guidance.