This has always puzzled me, why cabbage on St. Patrick's Day? Why not potatoes, a vegetable so much more identified with Ireland. Frankly I've always thought of cabbage as more of a German side dish to the groaning boards of hearty meats found in that country.
But, it seems, cabbage has long been part of Irish meals.
"Cabbage, thought to be distributed throughout Northern Europe by the Celts, thrived once it reached the cool climate of the Irish Isle and soon became an important source of nourishment throughout Ireland. As few crops could withstand the bad weather, greens such as cabbage and kale, along with leeks and onions, could be stored in dry barns, were the main source of food in the 12th through 16th centuries." During the potato famine, cabbage once again became the main source of sustenance.
So there you have it. The other question about corned beef is saved for another time.