The stories, as the title indicates, are linked together by the Dublin (Irish) experience as Joyce understood it. They are also linked by the experimental method Joyce used to end each story. Instead of finishing with the resolution of an external problem, the stories end at a moment of insight the main character experiences. Joyce called this moment an epiphany.
For example, the story "Araby," often read as a stand-alone tale, ends with the boy narrator's anguished realization he can't escape the sordid reality of Dublin for the world of his dreams. It seems to end abruptly, in mid-stream. We don't know what happens, for instance, between the narrator and the girl, Mangan's sister, he wanted to impress, because that does not matter. What matters is his emotional realization. Likewise, in the long final story of the book, "The Dead," Gabriel realizes that the dead are part of us, the living. This doesn't necessarily resolve the sudden tension he feels with his wife over her former beloved, but it does mean that Gabriel has experienced inner growth.
The term epiphany comes from the day the magi went to visit the infant Jesus with gifts, realizing he was the foretold Messiah. This biblical tale is a hopeful story of positive insight. Therefore, the epiphanies these characters experience, though painful, can be framed by the larger context of the hope for spiritual renewal they foreshadow.