There's an epiphany in The Dead when Gabriel understands that his life was lived in a passive way and that he'll never be loved like Michael Fury. It starts when Gretta listens a music that reminds her Michael Fury, her first love. Thanks to the epiphany activated by the song Gabriel sees how Gretta is moved by it and when he goes back to the hotel he wants to know why.
The epiphany makes someone understand more about the hidden parts of himself, thanks to a deep reflection. Furthermore, it is a moment of light, as now Gabriel understands he'll never be loved like Michael Fury, but also he also recognizes that he has never loved his wife in a furious way. Before the epiphany Gabriel is overprotective, pathetic, full of weaknesses and stuck on a role others give to him.
Joyce uses the interior monologue, a 3rd person omniscient narrator who doesn't comment what's happening, as he tells the story as if it were in the character's consciousness. Therefore, the 3rd person narrator represents reality by symbolical realism, as he wants the reader to understand there's a meaning beyond the surface of words.
In the speech Gabriel says that whenever we do rituals, our mind is crossed by sadness. Furthermore, he's trying by rhetorical means to convince his audience that life is full of memories, also of the dead, but he also states that people have to go on living. The speech will prove to be wrong after the epiphany, when Gabriel will discover the real feelings of Gretta.
What we know about Gretta comes from different points of view, the most frequent one is Gabriel's, who loves her more than she does.