The Merman is grieving because his wife has left and not returned. In the first stanza, he calls to his children to return to the sea with him. In the second stanza, he tells them to call out to their mother. He thinks that if their mother, Margaret, hears their "dear" voices, she will be compelled to return to them (and him). This continues in the third stanza. In the fourth stanza, the Merman cannot wait any longer. He tells the children to stop calling for their mother and they leave the land and return to the sea.
The Merman is so sad that he can't recall how long it's been since his wife has been gone. In the sixth stanza, he recalls the time she went on land for spiritual reasons: Easter. In the seventh stanza, the Merman recounts how he and the children left the sea and went on land to find her, but Margaret is too focused on spiritual matters by this point. In the eighth stanza, he and the children reluctantly return to the sea without her.
In the next stanza, Margaret is singing to herself while sewing. She drops her spindle and goes to the window. She looks longingly at the sea, an indication that she does miss her family. In the next stanza, the Merman tells the children that Margaret will continue to be haunted by the sounds of the sea.
Margaret has chosen life on land because it is the place where she connects with religion. Her faith has led her back there. However, she will continue to be conflicted about this decision, so the poem isn't just a statement about a woman choosing a religious life over a magical or romantic one. It also shows Margaret's uncertainty about the choice and therefore her uncertainty about her faith.
In the final stanza, the Merman foresees times in the future when he and his children will gaze at the town. He suggests that this feeling of being abandoned will emerge each time they look upon the land:
"There dwells a loved one,
But cruel is she!
She left lonely for ever
The kings of the sea."