“Symbol” isn’t exactly the right word—“archetype” is better.  Maurya, struggling with the economic hardships of raising a family without a husband, goes through the universal pangs of motherhood as her children grow up into the world and slip out of her protective grasp, only to be claimed by the forces outside her control (here, the sea).  The unfeeling universe does not differentiate between its victims, but Maurya can, by the unique sweater pattern of the family and by the “missed stitch” that gives Michael his unique signature.  Mixed into Maurya’s (and all mothers’) raising of her children is a belief in the supernatural/religious “justice” of the universe, so that (and this is what gives this play such poignancy) she can quickly resign herself to the “tragedies” that overtake the male members of the family, grieving but not resisting (Bartley’s ghost ride, and the last line of the play dramatize this).  The domestic setting of the sisters, while socially out of date now, is a typical situation in 20th (and earlier) century in peasant families, and is archetypical as well.  Synge’s genius put the play’s mise-en-scene beautifully in the Aran Islands fishing community, so that we get a portrait of this specific family, but his themes and his mother character are universal.  All mothers send their children out into the world to become “riders to the sea.”