In just a few lines, the poem sets up a paradox: a meal that feeds no one. The "dinner of air" is offered "for an old man," and the phrase can be read two ways. It might be a meal meant for an old man, or a joke about what an old man is expected to settle for. Either way, the food is empty.
The second stanza makes the point physical. The speaker eats "and eat[s]" with no end to it, yet comes home "thinner" rather than fuller. The repetition suggests hunger that never gets answered. Judging by the wording, the speaker could be talking about real scarcity, or about something less tangible, such as attention, comfort, or meaning that looks like nourishment but isn't.
The mood is spare, wry, and a little sad. There's a dry humor in the idea of dining on air, but the humor has a bitter edge. The short lines and plain words make the loss feel quiet and matter-of-fact, as if the speaker has already grown used to it.