He may be standing out in a country field by himself, but make no mistake: our speaker is there to do a job. It's an odd job by our modern standards, we admit. When we mow the lawn, we rely on a machine to do most of the work. At the turn of the twentieth century, though, things were done by hand. In fact, it takes two people to mow a field: one to cut, one to spread the cut grass so that it dries (either for hay or fertilizer). It's through this work, though, that the speaker feels a sense of connection to the mower. This is one life-affirming chore.
Lines 1-2: The mower's job is already done (he started at dawn, the early bird), and now the speaker's turn to work has come.
Line 10: The speaker thinks of himself as totally isolated. He describes this using an image of work. Even working together, he thinks folks are hopelessly separate from one another.
Line 36: After discovering the tuft of flowers, the speaker's totally changed his tune. Presented with the evidence of the mower's presence (the spared flowers), he feels a sense of connection in his work.
Lines 41-42: The poem's last couplet strikes a hopeful note for us all, still using the imagery of work. It makes sense, really. The things that people make in their work (ideas or products) can totally reach us—even if the people themselves can't. That's still connection, though, which is the point the speaker ends with here.