The shortbread recipe has changed throughout its history, and although there is a unique version from Ireland, the original shortbread you're familiar with comes from Scotland.
Its history is over a millennia old, dating back to the Middle Ages tradition of "biscuit bread," whereby excess dough was left in an oven on low heat until it hardened.
Over time, the yeast in the recipe was replaced with butter, and the dish got its name from the one-part sugar to two-part butter ratio, creating a crumbly or "short" texture.