My family has been Irish-American since the potato blight of the late 1840's but I'll try to give a rough explanation.
The green is for the Catholics, the orange the Protestants, and the white unity between the two.
The Dutch and the English fought the Irish and French in Ireland over the crown that once belonged to the Catholic King James (often referred to as Séamus an Chaca (James the Sh*t)). The decisive battle was fought at Aughrim and makes for a particularly interesting story from the days of King James. Oliver Cromwell is likely the most vilified of the English authorities. Vikings and Norman English forces had conquered previously but didn't try to eradicate the culture like the English did following that time. You couldn't speak the Irish tongue nor practice the Catholic religion and keep your land under the Penal Laws. This is tip of the iceberg stuff, of course, and I'd recommend people study up online, at least, if they're interested. I know I didn't get much of an education as to Ireland in American schools. It's somewhat maddening that people don't know Ireland had enough (non-tuber) food to feed itself during the so-called "famine," for example.
p.s. - This was a cool site that gives you a lot in very little space:
Irish History
