means The quality or state of being uneven, inconsistent, or not conforming to an expected rule, order, or shape — or a specific instance of such a deviation.

from Built from the Latin 'regula,' a straightedge or ruler — the literal stick by which carpenters and masons checked their lines. From 'regula' came 'regularis' (according to rule), and slapping on the negating prefix 'in-' gave 'irregularis,' the not-by-the-ruler. English borrowed the adjective 'irregular' from Old French in the late medieval period, then the abstract noun 'irregularity' grew the usual '-ity' tail. So at its root, an irregularity is simply anything that won't lie flat against the measuring rod.