A reverie is a state of being lost in thought. This tends to be associated with a pleasant daydreaming but it can also be melancholy. This essay contains feelings of fond remembrance, longing, and, in the end, sadness.
The speaker recalls beloved relatives from his past: great-grandmother Field and Uncle John. He recalls his seven year courtship of Alice which was characterized as full of hope, despair, and denial. All during his monologue, the speaker claims that he is telling these old stories to children of his own: John and Alice. He explains that "children love to hear stories about their elders." Just as he used to hear about his elders, he now tells tales to his children.
There is a twist at the end of the essay. As it turns out, the speaker's children, John and Alice, are figments of his imagination. He imagines his dream child, Alice, explaining to him:
We are nothing; less than nothing, and dreams. We are only what might have been, and must wait upon the tedious shores of Lethe millions of ages before we have existence, and a name”—and immediately awaking, I found myself quietly seated in my bachelor armchair, where I had fallen asleep, with the faithful Bridget unchanged by my side—but John L. (or James Elia) was gone forever.
The speaker never had children with the older Alice. Their courtship ended after seven years. The speaker has been lost in a daydream, in a reverie, the entire time. This essay is particularly successful because this realization that it has all been a daydream doesn't happen until the end. The reader gets lost in the speaker's tale, thinking it is real. The twist ending reveals it has all been a dream. His "bachelor armchair" indicates he is not married. And his only companion, Bridget, is possibly his dog.