In the opening stanza of the poem, the speaker says that there is a woman singing to him and that this woman's singing reminds him of when he was a boy and his mother used to sing to him. The speaker loses himself in this memory from the past. He recalls sitting "under the piano" and "pressing the small, poised feet of a mother who smiles as she sings." In other words, the speaker has been reminded of his mother playing the piano and singing for him when he was a very small boy.
Remembering these "Sunday evenings" with his mother, the speaker becomes very nostalgic. He longs to be back at the piano and with his mother. His heart, he says, "weeps to belong" once more to those evenings from his childhood. He describes those evenings as "cosy."
In the final stanza of the poem, the speaker says that the woman singing to him is singing in "vain," meaning that her singing no longer has any impact upon him, because he has become so absorbed in his memories. He says that "the glamour / Of childish days is upon" him, implying that he is perhaps trapped beneath the nostalgic weight of these memories. The implication is that he cannot tear himself away from his memories of those Sunday mornings at his mother's feet, even if he wanted to. These memories are so powerful that they are like "a flood," suggesting that the speaker has been swept away by them.
The final line of the poem states, "I weep like a child for the past." From the previous stanzas we might infer that the speaker weeps "like a child" because he is so sad that he can never truly experience, firsthand, those childhood memories ever again. He can never again be with his mother. Perhaps he also weeps, however, because he cannot fully appreciate or live in the present because of the irrepressible pull of his past.