A person born in America that is of Irish descent. Despite what others seem to think, an Irish-American person may have not been to Ireland, but this does not deny the existence of Irish in their blood. Millions of Irish immigrants fled to America even until the 1930's and settled thus creating families and spreading their blood lines. If ones' great grandparents or such came from Ireland, does that Irish blood not carry on to them even though they happened to born in America? Someone could easily have Irish parents and be born in Russia, or anywhere for that matter, but they are are still Irish no matter what country they happen enter the world into.
These are just a few great Irish-Americans. Ronald Reagan, James Cagney, Errol Flynn, Frank & Malachy McCourt, and many other greats.