The speaker sits reading, so absorbed that the afternoon slips away without notice. The poem's three short lines capture that feeling of losing track of everything else. "Engrossed" in the title tells us exactly what state the speaker is in, and the poem then shows us the consequences.
The funny turn comes in the last line. The dinner, "by and by" waiting to be eaten, is "gone with the ants." The wording suggests the meal was left out, and while the reader's attention was elsewhere, tiny insects carried it off. It's a small, domestic loss, and the speaker doesn't seem to mind much.
The mood is light, wry and affectionate. There is gentle humor in the idea that books can be so compelling that a meal disappears unnoticed. At the same time, the poem hints at a quiet contrast: the speaker feeds the mind while the ants feed the body, and both are content.