From 1649–50 Oliver Cromwell led a Parliamentary invasion of Ireland. Many Catholic landholders were dispossessed and forced to take their families and belongings beyond the Shannon, to the hard country of Connaught while English and Scottish Protestant newcomers settled on the lusher vacated farms, the dispossessed Irish hacked out a thin living among the ‘rocks, bogs, salt water and seaweed’ of the barren west coast. In the ensuing centuries, to many a farm-hand even the British Army offered better prospects than the stony plough-defying soil of Mayo, Galway and Clare. The lament of the Connaught ploughman has become a popular Irish folk songs. So, basically, whether or not there are actually Rocks of Bawn somewhere, “to plow the Rocks of Bawn” means to struggle tirelessly and thanklessly.
I learned this from the Clancys.