The Lawnmower Man is a cheesy '90s sci-fi flick, but it's also a handy nickname for our speaker. Actually, this guy is one of two lawnmower men. He's basically the sweeper (or turner-over), while the mower is already done with his work and is now nowhere to be found.
Of course, we're just guessing that the speaker and his chore-buddy are men. There's really no detail in the poem to clarify gender one way or another. We do know, though, that Frost based a lot of the poems in A Boy's Will on his own personal experiences, which probably would have included mowing a field by hand when he tried to be a farmer in New Hampshire.
Beyond that, though, we're really just left with the speaker's thoughts. He has two of them in this poem, and they're diametrically opposed to one another. Thought #1 goes like this: "We are, each of us, utterly alone in the world. Even if we're right next to someone, we can never truly experience a connection to that person." Pretty cheery, eh?
Don't get too far down in the dumps, though. Once he discovers that the absent mower has left behind a tuft of butterfly weed, our speaker's singing a whole different tune. Thought #2 says that, "We are, each of us, totally connected to one another through the evidence of our work in the world. Even if we're not physically together, the ideas and contributions we leave behind still connect us." Feel better now?
The speaker leaves off on that optimistic note, which makes this poem pretty rare by modern standards. Most poetry these days is grim and grimmer. But our speaker seems to have a genuine change of heart here. And it doesn't really strike us as wishful thinking. If you think about it, the products of others' work and ideas really do reach us, even across miles, years, and cultures. In that way, we are undeniably connected to many more people that perhaps we realized.
Thanks to a plucky butterfly and a lucky discovery of flowers, then, our speaker's entire worldview is transformed. This change of heart just goes to show that it pays to keep your eyes open—even when you're doing chores.