What are the Three Graces in the story "The Dead"?
To understand Joyce's allusion, you should know a bit about the classical graces to whom he is referring. The Three Graces, celebrated in classical literature and art, were the daughters of Jupiter (or Zeus in Greek mythology), and companions to the Muses. Thalia (youth and beauty) is accompanied by Euphrosyne (mirth), and Aglaia (elegance).
We think of the Muses as young and beautiful but it is clear that these women have gone past their prime. The overall impression is that they are "fussy." Aunt Julia is described as a "woman who does not know where she's going." Kate is "too feeble to go out" and Mary Jane, once a music teacher, has long been surpassed by her pupils. The women appear to live comfortably, but their fussing seems rather pointless.