Maurya has a terrifying vision in which she claims to have seen her late son Michael riding behind her only living son, Bartley, as he sails to Connemara to sell a horse. This turns out to be a premonition, as during his journey, Bartley falls from his horse into the sea and drowns, leaving Maurya entirely bereft of children. Maurya's premonition references the Four Horsemen of the Apocalypse in the Biblical Book of Revelation. Two of the Horsemen are alluded to in Maurya's vision: one riding a red horse, capable of taking away peace (Bartley), and another riding a pale horse (Death, as represented by the figure of Michael).
The title is significant in another respect. We normally associate sailing with the sea, not riding. One could argue that Synge uses the title Riders to the Sea to highlight the futility of Bartley's fateful journey. He's a rider, not a sailor, and as such is doomed to a premature end beneath the waves.